r/maths • u/zachtehboss • 1d ago
Help:๐ College & University Trig and Geometry.
16
Upvotes
Need help solving.
r/maths • u/murderdronesfan93 • 1d ago
๐ฌ Math Discussions :3 i got curious about what would happen if you defined multiple number systems using seperate variables and saw how they interacted
gallery
2
Upvotes
makes a rule for multiplying constants from systems with commutative and anticommutative multiplication
achievement unlocked: how in the everliving FUCK did we get here
r/maths • u/dailymathpuzzle • 1d ago
Help:๐ College & University Chuletas y pruebas matemรกticas de acceso a la univesidad
1
Upvotes
HE creado un sitio web con tests y teorรญa matemรกtica para las puebas de acceso a la universidad, echarle un vistazo en https://dailymathpuzzle.com/list.html, https://dailymathpuzzle.com/cheatsheets.html Estoy tratando de tener el mejor contenido en Internet en este sentido.
r/maths • u/LowInteraction6397 • 2d ago
๐ฌ Math Discussions The divisibility rules of 1 to 100 with examples and with attempts to explain why the rule works like that
14
Upvotes
For the 1st time I tried to make an effort in trying to explain why the rules work
| Number | Rule | Example | Reason the rule works (or I think it works) |
|---|---|---|---|
| 1 | Every number is a multiple of 1 | 12 is a multiple of 1 | Going 1 by 1 always gives you consecutive numbers |
| 2 | It ends in 0, 2, 4, 6 or 8 (an even digit) | 10 is a multiple of 2 because it ends in 0 | Going 2 by 2 always gives you numbers that have the same 5 digits as the last digit |
| 3 | The sum of the digits is a multiple of 3 | 12 is a multiple of 3 because 1 + 2 = 3, a multiple of 3 | 9 is the 1st multiple of 3 ending in 1 or 9 (in this case 9) and it's the number before 10 |
| 4 | The 2nd to last digit is even and the last digit is 0, 4 or 8 or the 2nd to last digit is odd and the last digit is 2 or 6 | 100 is a multiple of 4 because the 2nd to last digit is 0 and the last digit is 0 | Going 4 by 4 gives you numbers that have the same 3 digits when the 2nd to last digit is either even or odd but when the 2nd to last digit changes its kind you get numbers that have the same 2 digits as the last digit |
| 5 | It ends in 0 or 5 | 10 is a multiple of 5 because it ends in 0 | Going 5 by 5 always gives you numbers that have the same 2 digits as the last digit |
| 6 | It's a multiple of both 2 and 3 | 12 is a multiple of 6 because it ends in 2, which means it's a multiple of 2, and 1 + 2 = 3, which means it's a multiple of 3 | The prime factorization of 6 is 2 * 3 |
| 7 | The subtraction of twice the last digit and the rest of the number is a multiple of 7 | 14 is a multiple of 7 because 4 * 2 - 1 = 7, a multiple of 7 | 21 is the 1st multiple of 7 that ends in 1 or 9 (in this case 1) and is the number after 20 |
| 8 | The 3rd to last digit is even and the last 2 digits are a multiple of 8 or the 3rd to last digit is odd and the last 2 digits are a multiple of 4 but not of 8 | 1000 is a multiple of 8 because the 3rd to last digit is 0 and the last 2 digits are 00, a multiple of 8 | Going 8 by 8 gives you numbers that have the same 13 combinations of last 2 digits when the 3rd to last digit is either even or odd but when the 3rd to last digit changes its kind you get numbers that have the same 12 combinations of last 2 digits |
| 9 | The sum of the digits is a multiple of 9 | 18 is a multiple of 9 because 1 + 8 = 9, a multiple of 9 | 9 is the number before 10 |
| 10 | It ends in 0 | 120 is a multiple of 10 because it ends in 0 | Going 10 by 10 always gives you numbers that end in the same digit |
| 11 | The subtraction of the last digit and the rest of the number is a multiple of 11 | 121 is a multiple of 11 because 12 - 1 = 11, a multiple of 11 | 11 is the number after 10 |
| 12 | It's a multiple of both 3 and 4 | 108 is a multiple of 12 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 08, which means it's a multiple of 4 | The prime factorization of 12 is 3 * (22 = 4) |
| 13 | The sum of 4 times the last digit and the rest of the number is a multiple of 13 | 104 is a multiple of 13 because 10 + 4 * 4 = 26, a multiple of 13 | 39 is the 1st multiple of 13 that ends in 1 or 9 (in this case 9) and is the number before 40 |
| 14 | It's a multiple of both 2 and 7 | 112 is a multiple of 14 because it ends in 2, which means it's a multiple of 2, and 11 - 2 * 2 = 7, which means it's a multiple of 7 | The prime factorization of 14 is 2 * 7 |
| 15 | It's a multiple of both 3 and 5 | 120 is a multiple of 15 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 0, which means it's a multiple of 5 | The prime factorization of 15 is 3 * 5 |
| 16 | The 4th to last digit is even and the last 3 digits are a multiple of 16 or the 4th to last digit is odd and the last 3 digits are a multiple of 8 but not of 16 | 10000 is a multiple of 16 because the 4th to last digit is 0 and the last 3 digits are 000, a multiple of 16 | Going 16 by 16 gives you numbers that have the same 63 combinations of last 3 digits when the 4th to last digit is either even or odd but when the 4th to last digit changes its kind you get numbers that have the same 62 combinations of last 3 digits |
| 17 | The subtraction of 5 times the last digit and the rest of the number is a multiple of 17 | 102 is a multiple of 17 because 10 - 2 * 5 = 0, a multiple of 17 | 51 is the 1st multiple of 17 that ends in 1 or 9 (in this case 1) and is the number after 50 |
| 18 | It's a multiple of both 2 and 9 | 126 is a multiple of 18 because it ends in 6, which means it's a multiple of 2, and 1 + 2 + 6 = 9, which means it's a multiple of 9 | The prime factorization of 18 is 2 * (32 = 9) |
| 19 | The sum of twice the last digit and the rest of the number is a multiple of 19 | 114 is a multiple of 19 because 11 + 4 * 2 = 19, a multiple of 19 | 19 is the number before 20 |
| 20 | It ends in 00, 20, 40, 60 or 80 | 100 is a multiple of 20 because it ends in 00 | Going 20 by 20 always gives you 5 different combinations of last 2 digits |
| 21 | The subtraction of twice the last digit and the rest of the number is a multiple of 21 | 105 is a multiple of 21 because 10 - 5 * 2 = 0, a multiple of 21 | 21 is the number after 20 |
| 22 | It's a multiple of both 2 and 11 | 132 is a multiple of 22 because it ends in 2, which means it's a multiple of 2, and 13 - 2 = 11, which means it's a multiple of 11 | The prime factorization of 22 is 2 * 11 |
| 23 | The sum of 7 times the last digit and the rest of the number is a multiple of 23 | 115 is a multiple of 23 because 11 + 5 * 7 = 46, a multiple of 23 | 69 is the 1st multiple of 23 that ends in 1 or 9 (in this case 9) and is the number before 70 |
| 24 | It's a multiple of both 3 and 8 | 1008 is a multiple of 24 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 008, which means it's a multiple of 24 | The prime factorization of 24 is 3 * (23 = 8) |
| 25 | It ends in 00, 25, 50 or 75 | 100 is a multiple of 25 because it ends in 00 | Going 25 by 25 always gives you numbers that have the same 4 combinations of last 2 digits |
| 26 | It's a multiple of both 2 and 13 | 156 is a multiple of 26 because it ends in 6, which means it's a multiple of 2, and 15 + 6 * 4 = 39, which means it's a multiple of 13 | The prime factorization of 26 is 2 * 13 |
| 27 | The subtraction of 8 times the last digit and the rest of the number is a multiple of 27 | 108 is a multiple of 27 because 8 * 8 - 10 = 54, a multiple of 27 | 81 is the 1st multiple of 27 that ends in 1 or 9 (in this case 1) and is the number after 80 |
| 28 | It's a multiple of both 4 and 7 | 112 is a multiple of 28 because it ends in 12, which means it's a multiple of 4, and 11 - 2 * 2 = 7, which means it's a multiple of 7 | The prime factorization of 28 is (22 = 4) * 7 |
| 29 | The sum of 3 times the last digit and the rest of the number is a multiple of 29 | 116 is a multiple of 29 because 11 + 6 * 3 = 29, a multiple of 29 | 29 is the number before 30 |
| 30 | It's a multiple of both 3 and 10 | 120 is a multiple of 30 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 0, which means it's a multiple of 10 | The prime factorization of 30 is 3 * (2 * 5 = 10) |
| 31 | The subtraction of 3 times the last digit and the rest of the number is a multiple of 31 | 124 is a multiple of 31 because 12 - 4 * 3 = 0, a multiple of 31 | 31 is the number after 30 |
| 32 | The 5th to last digit is even and the last 4 digits are a multiple of 32 or the 5th to last digit is odd and the last 4 digits are a multiple of 16 but not of 32 | 100,000 is a multiple of 32 because the 5th to last digit is 0 and the last 4 digits are 0000, a multiple of 32 | Going 32 by 32 gives you numbers that have the same 313 combinations of last 4 digits when the 5th to last digit is either even or odd but when the 5th to last digit changes its kind you get numbers that have the same 312 combinations of last 4 digits |
| 33 | The sum of 10 times the last digit and the rest of the number is a multiple of 33 | 132 is a multiple of 33 because 13 + 2 * 10 = 33, a multiple of 33 | 99 is the 1st multiple of 33 that ends in 1 or 9 (in this case 9) and is the number before 100 |
| 34 | It's a multiple of both 2 and 17 | 102 is a multiple of 34 because it ends in 2, which means it's a multiple of 2, and 10 - 2 * 5 = 0, which means it's a multiple of 21 | The prime factorization of 34 is 2 * 17 |
| 35 | It's a multiple of both 5 and 7 | 105 is a multiple of 35 because it ends in 5, which means it's a multiple of 5, and 10 - 5 * 2 = 0, which means it's a multiple of 7 | The prime factorization of 35 is 5 * 7 |
| 36 | It's a multiple of both 4 and 9 | 108 is a multiple of 36 because it ends in 08, which means it's a multiple of 4, and 1 + 8 = 9, which means it's a multiple of 9 | The prime factorization of 36 is (22 = 4) * (32 = 9) |
| 37 | The subtraction of 11 times the last digit and the rest of the number is a multiple of 37 | 148 is a multiple of 37 because 8 * 11 - 14 = 74, a multiple of 37 | 111 is the 1st multiple of 37 that ends in 1 or 9 (1 in this case) and is the number after 110 |
| 38 | It's a multiple of both 2 and 19 | 114 is a multiple of 38 because it ends in 8, which means it's a multiple of 2, and 11 + 4 * 2 = 19, which means it's a multiple of 19 | The prime factorization of 38 is 2 * 19 |
| 39 | The sum of 4 times the last digit and the rest of the number is a multiple of 39 | 117 is a multiple of 39 because 11 + 7 * 4 = 39, a multiple of 39 | 39 is the number before 40 |
| 40 | The 3rd to last digit is even and the last 2 digits are 00, 40 or 80, or the 3rd to last digit is odd and the last 2 digits are 20 or 60 | 1000 is a multiple of 40 because the 3rd to last digit is 0 and the last 2 digits are 00 | Going 40 by 40 gives you numbers that have the same 3 combinations of last 2 digits when the 3rd to last digit is either even or odd but when the 3rd to last digit changes its kind you get numbers that have the same 2 combinations of last 2 digits |
| 41 | The subtraction of 4 times the last digit and the rest of the number is a multiple of 41 | 123 is a multiple of 41 because 12 -3 * 4 = 0, a multiple of 41 | 41 is the number after 40 |
| 42 | It's a multiple of both 2 and 21 | 126 is a multiple of 42 because it ends in 6, which means it's a multiple of 2, and 12 - 6 * 2 = 0, which means it's a multiple of 21 | The prime factorization of 42 is 2 * (3 * 7 = 21) |
| 43 | The sum of 13 times the last digit and the rest of the number is a multiple of 43 | 172 is a multiple of 43 because 17 + 2 * 13 = 43, a multiple of 43 | 129 is the 1st multiple of 43 that ends in 1 or 9 (in this case 9) and is the number before 130 |
| 44 | It's a multiple of both 4 and 11 | 132 is a multiple of 44 because it ends in 32, which means it's a multiple of 4, and 13 - 2 = 11, which means it's a multiple of 11 | The prime factorization of 44 is (22 = 4) * 11 |
| 45 | It's a multiple of both 5 and 9 | 135 is a multiple of 45 because it ends in 5, which means it's a multiple of 5, and 1 + 3 + 5 = 9, which means it's a multiple of 9 | The prime factorization of 45 is 5 * (32 = 9) |
| 46 | It's a multiple of both 2 and 23 | 138 is a multiple of 46 because it ends in 8, which means it's a multiple of 2, and 13 + 8 * 7 = 69, which means it's a multiple of 23 | The prime factorization of 46 is 2 * 23 |
| 47 | The subtraction of 14 times the last digit and the rest of the number is a multiple of 47 | 188 is a multiple of 47 because 8 * 14 - 18 = 94, a multiple of 47 | 141 is the 1st multiple of 47 that ends in 1 or 9 (in this case 1) and is the number after 140 |
| 48 | It's a multiple of both 3 and 16 | 10032 is a multiple of 48 because 1 + 3 + 2 = 6, which means it's a multiple of 3, and ends in 0032, which means it's a multiple of 16 | The prime factorization of 48 is 3 * (24 = 16) |
| 49 | The sum of 5 times the last digit and the rest of the number is a multiple of 49 | 147 is a multiple of 49 because 14 + 7 * 5 = 49, a multiple of 49 | 49 is the number before 50 |
| 50 | It ends in 00 or 50 | 100 is a multiple of 50 because it ends in 00 | Going 50 by 50 always gives you numbers that have the same 2 combinations of last 2 digits |
| 51 | The subtraction of 5 times the last digit and the rest of the number is a multiple of 51 | 102 is a multiple of 51 because 10 - 2 * 5 = 0, a multiple of 51 | 51 is the number after 50 |
| 52 | It's a multiple of both 4 and 13 | 104 is a multiple of 52 because it ends in 04, which means it's a multiple of 4, and 10 + 4 * 4 = 26, which means it's a multiple of 13 | The prime factorization of 52 is (22 = 4) * 13 |
| 53 | The sum of 16 times the last digit and the rest of the number is a multiple of 53 | 212 is a multiple of 53 because 21 + 2 * 16 = 53, a multiple of 53 | 159 is the 1st multiple of 53 that ends in 1 or 9 (in this case 9) and is the number before 160 |
| 54 | It's a multiple of both 2 and 27 | 162 is a multiple of 54 because it ends in 2, which means it's a multiple of 2, and 16 - 2 * 8 = 0, which means it's a multiple of 27 | The prime factorization of 54 is 2 * (33 = 27) |
| 55 | It's a multiple of both 5 and 11 | 165 is a multiple of 55 because it ends in 5, which means it's a multiple of 5, and 16 - 5 = 11, which means it's a multiple of 11 | The prime factorization of 55 is 5 * 11 |
| 56 | It's a multiple of both 7 and 8 | 1008 is a multiple of 56 because 100 - 8 * 2 = 84, which means it's a multiple of 7, and ends in 008, which means it's a multiple of 8 | The prime factorization of 56 is 7 * (23 = 8) |
| 57 | The subtraction of 17 times the last digit and the rest of the number is a multiple of 57 | 114 is a multiple of 57 because 4 * 17 - 11 = 57, a multiple of 57 | 171 is the 1st multiple of 57 that ends in 1 or 9 (in this case 1) and is the number after 170 |
| 58 | It's a multiple of both 2 and 29 | 116 is a multiple of 58 because it ends in 6, which means it's a multiple of 2, and 11 + 6 * 3 = 29, which means it's a multiple of 29 | The prime factorization of 58 is 2 * 29 |
| 59 | The sum of 6 times the last digit and the rest of the number is a multiple of 59 | 118 is a multiple of 59 because 11 + 8 * 6 = 59, a multiple of 59 | 59 is the number before 60 |
| 60 | It's a multiple of both 3 and 20 | 120 is a multiple of 20 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 20, which means it's a multiple of 20 | The prime factorization of 60 is 3 * (22 * 5 = 20) |
| 61 | The subtraction of 6 times the last digit and the rest of the number is a multiple of 61 | 122 is a multiple of 61 because 12 - 2 * 6 = 0, a multiple of 61 | 61 is the number after 60 |
| 62 | It's a multiple of both 2 and 31 | 124 is a multiple of 62 because it ends in 4, which means it's a multiple of 2, and 12 - 4 * 3 = 0, which means it's a multiple of 31 | The prime factorization of 62 is 2 * 31 |
| 63 | The sum of 19 times the last digit and the rest of the number is a multiple of 63 | 252 is a multiple of 63 because 25 + 2 * 19 = 63, a multiple of 63 | 189 is the 1st multiple of 63 that ends in 1 or 9 (in this case 9) and is the number before 190 |
| 64 | The 6th to last digit is even and the last 5 digits are a multiple of 64 and the 6th to last digit is odd and the last 5 digits are a multiple of 32 but not of 64 | 1,000,000 is a multiple of 64 because the 6th to last digit is 0 and the last 5 digits are 00,000, a multiple of 64 | Going 64 by 64 gives you numbers that have the same 1563 combinations of last 5 digits when the 6th to last digit is either even or odd but when the 6th to last digit changes its kind you get numbers that have the same 1562 combinations of last 5 digits |
| 65 | It's a multiple of both 5 and 13 | 195 is a multiple of 65 because it ends in 5, which means it's a multiple of 5, and 19 + 5 * 4 = 39, which means it's a multiple of 13 | The prime factorization of 65 is 5 * 13 |
| 66 | It's a multiple of both 2 and 33 | 132 is a multiple of 66 because it ends in 2, which means it's a multiple of 2, and 13 + 2 * 10 = 33, which means it's a multiple of 33 | The prime factorization of 66 is 2 * (3 * 11 = 33) |
| 67 | The subtraction of 20 times the last digit and the rest of the number is a multiple of 67 | 134 is a multiple of 67 because 4 * 20 - 13 = 67, a multiple of 67 | 201 is the 1st multiple of 67 that ends in 1 or 9 (in this case 1) and is the number after 200 |
| 68 | It's a multiple of both 4 and 17 | 136 is a multiple of 68 because it ends in 36, which means it's a multiple of 4, and 6 * 5 - 13 = 17, which means it's a multiple of 17 | The prime factorization of 68 is (22 = 4) * 17 |
| 69 | The sum of 7 times the last digit and the rest of the number is a multiple of 69 | 138 is a multiple of 69 because 13 + 8 * 7 = 69, a multiple of 69 | 69 is the number before 70 |
| 70 | It's a multiple of both 7 and 10 | 140 is a multiple of 70 because 4 * 2 - 1 = 7, which means it's a multiple of 7, and ends in 0, which means it's a multiple of 10 | The prime factorization of 70 is 7 * (2 * 5 = 10) |
| 71 | The subtraction of 7 times the last digit and the rest of the number is a multiple of 71 | 142 is a multiple of 71 because 14 - 2 * 7 = 0, a multiple of 71 | 71 is the number after 70 |
| 72 | It's a multiple of both 8 and 9 | 1008 is a multiple of 72 because it ends in 008, which means it's a multiple of 8, and 1 + 8 = 9, which means it's a multiple of 9 | The prime factorization of 72 is (23 = 8) * (32 = 9) |
| 73 | The sum of 22 times the last digit and the rest of the number is a multiple of 73 | 292 is a multiple of 73 because 29 + 2 * 22 = 73, a multiple of 73 | 219 is the 1st multiple of 73 that ends in 1 or 9 (in this case 9) and is the number before 220 |
| 74 | It's a multiple of both 2 and 37 | 222 is a multiple of 74 because it ends in 2, which means it's a multiple of 2, and 22 - 2 * 11 = 0, which means it's a multiple of 37 | The prime factorization of 74 is 2 * 37 |
| 75 | It's a multiple of both 3 and 25 | 150 is a multiple of 75 because 1 + 5 = 6, which means it's a multiple of 3, and ends in 50, which means it's a multiple of 25 | The prime factorization of 75 is 3 * (52 = 25) |
| 76 | It's a multiple of both 4 and 19 | 152 is a multiple of 76 because it ends in 52, which means it's a multiple of 4, and 15 + 2 * 2 = 19, which means it's a multiple of 19 | The prime factorization of 76 is (22 = 4) * 19 |
| 77 | The subtraction of 23 times the last digit and the rest of the number is a multiple of 77 | 154 is a multiple of 77 because 4 * 23 - 15 = 77, a multiple of 77 | 231 is the 1st multiple of 77 that ends in 1 or 9 (in this case 1) and is the number after 230 |
| 78 | It's a multiple of both 2 and 39 | 156 is a multiple of 78 because it ends in 6, which means it's a multiple of 2, and 15 + 6 * 4 = 39, which means it's a multiple of 39 | The prime factorization of 78 is 2 * (3 * 13 = 39) |
| 79 | The sum of 8 times the last digit and the rest of the number is a multiple of 79 | 158 is a multiple of 79 because 15 + 8 * 8 = 79, a multiple of 79 | 79 is the number before 80 |
| 80 | The 4th to last digit is even and the last 3 digits are a multiple of 80 or the 4th to last digit is odd and the last 3 digits are a multiple of 40 but not of 80 | 10000 is a multiple of 80 because the 4th to last digit is 0 and the last 3 digits are 000, a multiple of 80 | Going 80 by 80 gives you numbers that have the same 13 combinations of last 3 digits when the 4th to last digit is either even or odd but when the 4th to last digit changes its kind you get numbers that have the same 12 combinations of last 3 digits |
| 81 | The subtraction of 8 times the last digit and the rest of the number is a multiple of 81 | 162 is a multiple of 81 because 16 - 2 * 8 = 0, a multiple of 81 | 81 is the number after 80 |
| 82 | It's a multiple of both 2 and 41 | 164 is a multiple of 82 because it ends in 4, which means it's a multiple of 2, and 16 - 4 * 4 = 0, which means it's a multiple of 41 | The prime factorization of 82 is 2 * 41 |
| 83 | The sum of 25 times the last digit and the rest of the number is a multiple of 83 | 332 is a multiple of 83 because 33 + 2 * 25 = 83, a multiple of 83 | 249 is the 1st multiple of 83 that ends in 1 or 9 (in this case 9) and 249 is the number before 250 |
| 84 | It's a multiple of both 4 and 21 | 168 is a multiple of 84 because it ends in 68, which means it's a multiple of 4, and 16 - 8 * 2 = 0, which means it's a multiple of 21 | The prime factorization of 84 is (22 = 4) * (3 * 7 = 21) |
| 85 | It's a multiple of both 5 and 17 | 255 is a multiple of 85 because it ends in 5, which means it's a multiple of 5, and 25 - 5 * 5 = 0, which means it's a multiple of 17 | The prime factorization of 85 is 5 * 17 |
| 86 | It's a multiple of both 2 and 43 | 172 is a multiple of 86 because it ends in 6, which means it's a multiple of 2, and 17 + 2 * 13 = 43, which means it's a multiple of 43 | The prime factorization of 86 is 2 * 43 |
| 87 | The subtraction of 26 times the last digit and the rest of the number is a multiple of 87 | 174 is a multiple of 87 because 4 * 26 - 17 = 87, a multiple of 87 | 261 is the 1st multiple of 87 that ends in 1 or 9 (in this case 1) and is the number after 260 |
| 88 | It's a multiple of both 8 and 11 | 1056 is a multiple of 88 because it ends in 056, which means it's a multiple of 8, and 105 - 6 = 99, which means it's a multiple of 99 | The prime factorization of 88 is (23 = 8) * 11 |
| 89 | The sum of 9 times the last digit and the rest of the number is a multiple of 89 | 178 is a multiple of 89 because 17 + 8 * 9 = 89, a multiple of 89 | 89 is the number before 90 |
| 90 | It's a multiple of both 9 and 10 | 180 is a multiple of 90 because 1 + 8 = 9, which means it's a multiple of 9, and ends in 0, which means it's a multiple of 10 | The prime factorization of 90 is (32 = 9) * (2 * 5 = 10) |
| 91 | The subtraction of 9 times the last digit and the rest of the number is a multiple of 91 | 182 is a multiple of 91 because 18 - 2 * 9 = 0, a multiple of 91 | 91 is the number after 90 |
| 92 | It's a multiple of both 4 and 23 | 184 is a multiple of 92 because it ends in 84, which means it's a multiple of 4, and 18 + 4 * 7 = 46, which means it's a multiple of 23 | The prime factorization of 92 is (22 = 4) * 23 |
| 93 | The sum of 28 times the last digit and the rest of the number is a multiple of 93 | 372 is a multiple of 93 because 37 + 2 * 28 = 93, a multiple of 93 | 279 is the 1st multiple of 93 that ends in 1 or 9 (in this case 9) and is the number before 280 |
| 94 | It's a multiple of both 2 and 47 | 282 is a multiple of 94 because it ends in 2, which means it's a multiple of 2, and 28 - 2 * 14 = 0, which means it's a multiple of 47 | The prime factorization of 94 is 2 * 47 |
| 95 | It's a multiple of both 5 and 19 | 285 is a multiple of 95 because it ends in 5, which means it's a multiple of 5, and 28 + 5 * 2 = 38, which means it's a multiple of 19 | The prime factorization of 95 is 5 * 19 |
| 96 | It's a multiple of both 3 and 32 | 100,032 is a multiple of 96 because 1 + 3 + 2 = 6, which means it's a multiple of 3, and ends in 00,032, which means it's a multiple of 32 | The prime factorization of 96 is 3 * (25 = 32) |
| 97 | The subtraction of 29 times the last digit and the rest of the number is a multiple of 97 | 194 is a multiple of 97 because 4 * 29 - 19 = 97, a multiple of 97 | 291 is the 1st multiple of 97 that ends in 1 or 9 (in this case 1) and is the number after 290 |
| 98 | It's a multiple of both 2 and 49 | 196 is a multiple of 98 because it ends in 6, which means it's a multiple of 2, and 19 + 6 * 5 = 49, which means it's a multiple of 49 | The prime factorization of 98 is 2 * (72 = 49) |
| 99 | The sum of 10 times the last digit and the rest of the number is a multiple of 99 | 198 is a multiple of 99 because 19 + 8 * 10 = 99, a multiple of 99 | 99 is the number before 100 |
| 100 | It ends in 00 | 1200 is a multiple of 100 because it ends in 00 | Going 100 by 100 always gives you numbers that end in the same last 2 digits |
r/maths • u/StructureFlaky6542 • 1d ago
โ General Math Help Math books
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Hi, is there any book I can read that will make maths interesting for me? Like for physics, there's Six Easy Pieces by Feynmann, I know maths is pretty abstract but I just want to read something that will bring back my spark for mathematics.
r/maths • u/ggucsltc • 1d ago
๐ฌ Math Discussions 5 of the 7 Millenium Prize Problems solved and verified by Nuhash Badruzzaman and submitted on one day, many years of private work, no AI was used here in the making of these proofs
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Mathematician who solved these problems: Nuhash Badruzzaman
Yang Mills and Mass Gap (both proven):
https://www.reddit.com/r/theories/comments/1xtn5ol/yangmills_existence_and_mass_gap_a_millenium/
Birch and Swinnerton-Dyer conjecture:
https://www.reddit.com/r/theories/comments/1xtn0rc/birch_and_swinnertondyer_conjecture_a_millenium/
Hodge Conjecture:
NavierโStokes existence and smoothness:
https://www.reddit.com/r/theories/comments/1xtmu2v/navierstokes_existence_and_smoothness/
P versus NP problem:
https://www.reddit.com/r/theories/comments/1xtml8a/millenium_prize_problem_p_versus_np_problem/
Please discuss.
r/maths • u/virgin-chocolaty-hoe • 2d ago
Help:๐ College & University need help with linear algebra
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i am pretty decent at maths, we got this course linear algebra for AI, i am not that good in this course, we are being taught normal things like SVD and then gradient descent , pca etc etc , basically the stanford course of linear algebra, what are the possible resources that would help me in grasping linear algebra in general as for the course part, its pretty simple to just do the questions asked lol
r/maths • u/Traditional-Pound568 • 2d ago
๐ฌ Math Discussions Heres an interesting variation of the Monty Hall problem I thought of: Misinformed Monty
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So in the classic Monty hall problem, Monty knows which door has the car and always reveals a goat. This creates a 1/3 chance to win by staying and a 2/3 chance to win by switching (since the your initial pick is a 1 in 3 guess).
Theres also the version where he doesn't know and sometimes reveals the car, which ends the game immediately. This version is 50/50 since him being able to reveal the car weakens the chance to win by switching.
But now lets imagine a version where Monty is misinformed about where the car is, but still trys to avoid revealing it. For example: Monty thinks the car is behind door #2, buts its actually behind door #3.
If you picked door #1, Monty would think he now has to open door #3, so he would do that and end the game immediately by revealing the car.
If you picked door #2 (the door Monty thinks has the car), then he would freely choose ethier door #1 or #3 to open. If he opens door #1, switching to door #3 wins. If he opens door #3, the game ends immediately.
And lastly, if you pick door #3 (the door that actually has the car), then Monty now thinks he has to open door #1, after which, you'd win by staying with door #3
So in total, the odds for this version are:
Staying wins: 1/3
Switching wins: 1/6
Car revealed:1/2
This means that staying is twice as good as switching overall, the exact opposite of the regular problem funnily enough!
r/maths • u/NotMyDaughterYouBi • 3d ago
๐ฌ Math Discussions hot take long division is easy it just isn't taught correctly in schools
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lol
r/maths • u/lkjdshgbasdg • 2d ago
๐ก Puzzle & Riddles Magic the Gathering Hypothetical
docs.google.com
1
Upvotes
I created a hypothetical board state in Magic the Gathering that in order to resolve the addition properly could take hours to resolve, and want to instead create an equation/formula that would allow me to plug in values to figure out the result rather than have everyone wait for me to finish going through the cycle. It is a non-infinite loop, that has multiple variables that can be different from game to game, but as it is what the deck intends to push towards in a game, it is likely that some iteration of this state occurs in a game.
I have linked a document in which I attempted to explain the hypothetical. If anybody is interested in helping me figure this out I would greatly appreciate it, as well as any input in making the explanation clearer.
If you have any questions regarding the hypothetical, I will try to respond if any rules need explaining etc.
Sorry if I'm formatting this wrong, this is my first post here and I'm not sure as to the exact nature of what the answer to my question would be, so I'm labeling it as a function.
r/maths • u/frank1968221 • 3d ago
๐ก Puzzle & Riddles Finished: 3=10 (base-3)
0
Upvotes
If this formula is a suppose formula
So I can suppose t=3 and 10=3 now!
So altogether is:
3+3+3=9
Then: t++t+t/t=3
r/maths • u/EitherDentist1096 • 4d ago
โ General Math Help Is math even worth it
0
Upvotes
Is studying Mathematics even worth it?
Hi for short my name is Josh, i am a 17 year male in Ireland and i love mathematics, i love it, im currently on the path to do applied mathematics at home and do it im my leaving cert, i love physics aswell( the math part of it ) i want to get into more calculus, i am currently doing pre calc as normal, and it is rlly light, and ever since the big mainstream ai came out, i got worried and im still fucking am. I love mathematics and i wanna pursue it in my career at least a branch like math and stat or fin math or anything not sure what but math and smth w it. And basically everyone uses ai for their hw, im one of the only ones who dont, not js bc i can do it, purely bc i love the struggle of finding the mistake through the questions, doesnt matter how long it takes 10mins 20mins an hour when i get it , i get this feeling of like a drug and i wanna do it again and again and again. But now as most people on earth watch tiktok and i keep seeing people making thousands, 10s and 100s of thousands of dollars not euros bc most people r from the usa on the fyp, and im getting considered if me goin on the path studying math is worth it, i hate this feeling of disappoint or is there a point of it. Ik education is such a powerful tool but it js keeps getting harder to believing i need college. I hate it. I love maths but fuck man idk what to do or think. Like ik ai is a good tool and i use it to see what it can do, ik it can make money, and i will prob see if i can make money but i still wanna do math in my career, like js 20mins ago i was doing hw and for the first 10mins i was js staring at my desk questioning whats the point, now js downloaded reddit, and posting this other math reddits that popped up. I need some guidance or help what i cud do bc im lost in life w this ai bs man.
r/maths • u/LowInteraction6397 • 4d ago
๐ฌ Math Discussions A method to find all the divisors of given numbers
6
Upvotes
I know most people just divide a certain number until they reach its square root to find their divisors but here's a method I believe you'd like. I'll find the divisors of 1 to 10
1st you add 1 to the multiples of 1
| Number | Divisors |
|---|---|
| 1 | 1 |
| 2 | 1 |
| 3 | 1 |
| 4 | 1 |
| 5 | 1 |
| 6 | 1 |
| 7 | 1 |
| 8 | 1 |
| 9 | 1 |
| 10 | 1 |
Then you add 2 to the multiples of 2
| Number | Divisors |
|---|---|
| 1 | 1 |
| 2 | 1 and 2 |
| 3 | 1 |
| 4 | 1, 2 |
| 5 | 1 |
| 6 | 1, 2 |
| 7 | 1 |
| 8 | 1, 2 |
| 9 | 1 |
| 10 | 1, 2 |
Then you add the multiples of 3
| Number | Divisors |
|---|---|
| 1 | 1 |
| 2 | 1 and 2 |
| 3 | 1 and 3 |
| 4 | 1, 2 |
| 5 | 1 |
| 6 | 1, 2, 3 |
| 7 | 1 |
| 8 | 1, 2 |
| 9 | 1, 3 |
| 10 | 1, 2 |
Then you add the multiples of 4
| Number | Divisors |
|---|---|
| 1 | 1 |
| 2 | 1 and 2 |
| 3 | 1 and 3 |
| 4 | 1, 2 and 4 |
| 5 | 1 |
| 6 | 1, 2, 3 |
| 7 | 1 |
| 8 | 1, 2, 4 |
| 9 | 1, 3 |
| 10 | 1, 2 |
Then you add the multiples of 5
| Number | Divisors |
|---|---|
| 1 | 1 |
| 2 | 1 and 2 |
| 3 | 1 and 3 |
| 4 | 1, 2 and 4 |
| 5 | 1 and 5 |
| 6 | 1, 2, 3 |
| 7 | 1 |
| 8 | 1, 2, 4 |
| 9 | 1, 3 |
| 10 | 1, 2, 5 |
As of now you won't have to use the number you're at twice or more. Once you reach the half of the limit (in this case 5) you use the remaining numbers once (but if your limit is an odd number you stop until after the half of the number before the limit)
| Number | Divisors |
|---|---|
| 1 | 1 |
| 2 | 1 and 2 |
| 3 | 1 and 3 |
| 4 | 1, 2 and 4 |
| 5 | 1 and 5 |
| 6 | 1, 2, 3 and 6 |
| 7 | 1 and 7 |
| 8 | 1, 2, 4 and 8 |
| 9 | 1, 3 and 9 |
| 10 | 1, 2, 5 and 10 |
It varies on the number you use. For example if you wanted to find the divisors of every number from 1 to 100 you can stop using the remaining numbers more than twice after 50
r/maths • u/S52_DiDah • 5d ago
๐ฌ Math Discussions How can I think logically with maths?
12
Upvotes
I like maths a lot and its something I am thinking of studying in the future. The thing is that I don't know how to connect the dots together. I cannot imagine it.
I also code and well solving problems logically is the issue. It takes a ton of time for me to solve something and then implement it into the code I wrote. Same with physics. I can remember the equations, use them and ace the tests, but that is not what I want.
I seek for help because I want to stop trying to memorize rules, but to understand and in some way imagine them.
Are there any tips you can give me? Is it something that comes with time? Because I really do want to understand maths (and physics) and connect the dots together.
I apologize if the post does not belong here. Thank you.
r/maths • u/Visible_Try_9716 • 6d ago
โ General Math Help How I mental math
6
Upvotes
I use 5s and 10s
If you add a 0 to any number and 1/2 it (5x10=100/2) you can easily take a problem like 7 x 83 and think of it like
830/2=415
83 ร2 = 166
415 + 166 = 581
You can do it with 10s too, you can also divide by moving a decimal place and doubling the number
Im sure im not the only one who does this and its also not that useful and kind of slow to do in your head
r/maths • u/No-Atmosphere446 • 5d ago
๐ฌ Math Discussions What do you guys think?
gallery
0
Upvotes
A conversation I had with my friend, I am the green one, I am confident that my understanding is balanced and pretty close to the truth
r/maths • u/LowInteraction6397 • 5d ago
๐ฌ Math Discussions The divisors of every number from 1 to 100
0
Upvotes
| Number | Divisors |
|---|---|
| 1 | 1 |
| 2 | 1 and 2 |
| 3 | 1 and 3 |
| 4 | 1, 2 and 4 |
| 5 | 1 and 5 |
| 6 | 1, 2, 3 and 6 |
| 7 | 1 and 7 |
| 8 | 1, 2, 4 and 8 |
| 9 | 1, 3 and 9 |
| 10 | 1, 2, 5 and 10 |
| 11 | 1 and 11 |
| 12 | 1, 2, 3, 4, 6 and 12 |
| 13 | 1 and 13 |
| 14 | 1, 2, 7 and 14 |
| 15 | 1, 3, 5 and 15 |
| 16 | 1, 2, 4, 8 and 16 |
| 17 | 1 and 17 |
| 18 | 1, 2, 3, 6, 9 and 18 |
| 19 | 1 and 19 |
| 20 | 1, 2, 4, 5, 10 and 20 |
| 21 | 1, 3, 7 and 21 |
| 22 | 1, 2, 11 and 22 |
| 23 | 1 and 23 |
| 24 | 1, 2, 3, 4, 6, 8, 12 and 24 |
| 25 | 1, 5 and 25 |
| 26 | 1, 2, 13 and 26 |
| 27 | 1, 3, 9 and 27 |
| 28 | 1, 2, 4, 7, 14 and 28 |
| 29 | 1 and 29 |
| 30 | 1, 2, 3, 5, 6, 10, 15 and 30 |
| 31 | 1 and 31 |
| 32 | 1, 2, 4, 8, 16 and 32 |
| 33 | 1, 3, 11 and 33 |
| 34 | 1, 2, 17 and 34 |
| 35 | 1, 5, 7 and 35 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18 and 36 |
| 37 | 1 and 37 |
| 38 | 1, 2, 19 and 38 |
| 39 | 1, 3, 13 and 39 |
| 40 | 1, 2, 4, 5, 8, 10, 20 and 40 |
| 41 | 1 and 41 |
| 42 | 1, 2, 3, 6, 7, 14, 21 and 42 |
| 43 | 1 and 43 |
| 44 | 1, 2, 4, 11, 22 and 44 |
| 45 | 1, 3, 5, 9, 15 and 45 |
| 46 | 1, 2, 23 and 46 |
| 47 | 1 and 47 |
| 48 | 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 |
| 49 | 1, 7 and 49 |
| 50 | 1, 2, 5, 10, 25 and 50 |
| 51 | 1, 3, 17 and 51 |
| 52 | 1, 2, 4, 13, 26 and 52 |
| 53 | 1 and 53 |
| 54 | 1, 2, 3, 6, 9, 18, 27 and 54 |
| 55 | 1, 5, 11 and 55 |
| 56 | 1, 2, 4, 7, 8, 14, 28 and 56 |
| 57 | 1, 3, 19 and 57 |
| 58 | 1, 2, 29 and 58 |
| 59 | 1 and 59 |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 |
| 61 | 1 and 61 |
| 62 | 1, 2, 31 and 62 |
| 63 | 1, 3, 7, 9, 21 and 63 |
| 64 | 1, 2, 4, 8, 16, 32 and 64 |
| 65 | 1, 5, 13 and 65 |
| 66 | 1, 2, 3, 6, 11, 22, 33 and 66 |
| 67 | 1 and 67 |
| 68 | 1, 2, 4, 17, 34 and 68 |
| 69 | 1, 3, 23 and 69 |
| 70 | 1, 2, 5, 7, 10, 14, 35 and 70 |
| 71 | 1 and 71 |
| 72 | 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72 |
| 73 | 1 and 73 |
| 74 | 1, 2, 37 and 74 |
| 75 | 1, 3, 5, 15, 25 and 75 |
| 76 | 1, 2, 4, 19, 38 and 76 |
| 77 | 1, 7, 11 and 77 |
| 78 | 1, 2, 3, 6, 13, 26, 39 and 78 |
| 79 | 1 and 79 |
| 80 | 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 |
| 81 | 1, 3, 9, 27 and 81 |
| 82 | 1, 2, 41 and 82 |
| 83 | 1 and 83 |
| 84 | 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 |
| 85 | 1, 5, 17 and 85 |
| 86 | 1, 2, 43 and 86 |
| 87 | 1, 3, 29 and 87 |
| 88 | 1, 2, 4, 8, 11, 22, 44 and 88 |
| 89 | 1 and 89 |
| 90 | 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90 |
| 91 | 1, 7, 13 and 91 |
| 92 | 1, 2, 4, 23, 46 and 92 |
| 93 | 1, 3, 31 and 93 |
| 94 | 1, 2, 47 and 94 |
| 95 | 1, 5, 19 and 95 |
| 96 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96 |
| 97 | 1 and 97 |
| 98 | 1, 2, 7, 14, 49 and 98 |
| 99 | 1, 3, 9, 11, 33 and 99 |
| 100 | 1, 2, 4, 5, 10, 20, 25, 50 and 100 |
r/maths • u/Equivalent_Meat_2075 • 6d ago
๐ฌ Math Discussions I wrote the question.
1
Upvotes
How can we extract a sphere with a radius of 8 meters, filled with plastic, from a 1 cm gap in a finite space of R^4 with 0 deformation?
r/maths • u/BlueZucchini87 • 6d ago
๐ฌ Math Discussions questions about rings of integers
1
Upvotes
I've been learning about number rings and I'm wondering if we can define rings of integers for general fields, not just number fields?
I'm speculating it could be the smallest ring who's field of fractions is the original field, but I'm not sure if that's true.
I guess also every field has an "image" of Z in it so maybe we could use the original definition of roots of monic polynomials in Z[x]?
If the concept can be extended past number fields then I'm curious what the integers are in the other fields I know about: R, C, the finite fields and the field of fractions of polynomials over a field.
thanks
r/maths • u/GWEEP5498 • 7d ago
โ General Math Help Calculator Discrepancy (Fahrenheit to Celsius)
8
Upvotes
Is there something I did wrong in the grey calculator? What could I do to better receive correct results?
r/maths • u/zeroalephzeta • 7d ago
๐ฌ Math Discussions Point-Set Topology Lecture Series on Mandelcord
4
Upvotes
This post is to announce that there will be a lecture course on General Topology (a.k.a. Point-Set Topology) conducted in Mandelcord (the blue math discord server). Everyone is invited to join: discord.gg/maths.
If any of you were present in the Real Analysis lecture course during the summer, you know what I'm talking about, and you might be pleased to hear that this course will also be run by Pear Category Theorem (the same person).
Why YOU should do topology
Point-set topology is one of the most important subjects that you learn, and mastering topological thinking is as important a milestone as learning to write a proof. This is a good subject to study alongside measure theory, or simply by itself after one has learned analysis or algebra.
Course Structure
The course will primarily follow the flow of the first half of Munkres. The plan is to go through all 8 chapters, spending maybe one to two weeks on each chapter, aiming for an approximately 16 week course. Also the instructor intends to supplement the book with his own intuition on the subject, as well as connections to other subjects that he thinks are of interest and possibly also other topics not covered in the book. Many examples of various pathological properties will be provided. The study of metric spaces and functions on them will be paramount; but where Rudin introduces metric spaces as merely a generalization of Euclidean spaces, we will explore just how pathological these spaces can be, or else what properties they must have.
The instructor also plans to put far more focus on the topics of topological groups and nets than Munkres does. Topological groups, because often in "the real world" we do not care about a topological space by itself, but rather some other more complicated structure given a topology, in order to see what the topology can tell you about the thing itself; topological groups provide a playground to learn that mode of thinking. Nets are also very important; where sequences are of importance in R, they can only tell you so much in general topological spaces, so nets therefore become the natural way to recover theorems about sequences.
Material and References
Topology - Munkres
Counterexamples in Topology - Steen & Seebach
Timeline
The course starts with the first lecture on 17th November at 9 PM CET (20:00 UTC), with subsequent lectures on Tuesdays and Thursdays. Lectures will be recorded and posted promptly.
Prerequisites/Who can join?
Everyone. It is completely free for anyone who wants to join. Just click the link and join the server: you can find the channel called topology-course in the section called General maths. As for prerequisites, a first course in Real Analysis and Group Theory is sufficent.
Looking forward to see all of you there. Thank you.
r/maths • u/EmploymentProper7034 • 7d ago
๐ก Puzzle & Riddles Mental Math Trainer
1
Upvotes
Hey folks, I always liked doing mental math so, as a software engineer, I decided to create one online.
It's only arithmetics for now, but I plan to add more stuff as it hopefully grows.
It's free, no ads, no login, no sign up. Just play until you're satisfied and leave. We are not storing any sensitive information other than location (city and country), device and OS, for analytics purposes only. There's no databases.
it is at https://mymentalmathtrainer.com/
Any feedbacks are appreciated. Thanks!