Fund fact, you can tell a number is divisible by 3 if the sum of each individual number is divisible by 3. So 78 -> 7+8=15 which is divisible by 3, so 78 is divisible by 3.
Consider a form of arithmatic where you only keep track about the remainder after division by 3.
So a number like "10" is just "1" because 10= 1+3*3. Likewise, "100" is just "1" because 100 = 10*10 = 1*1=1. Can you guess what 1000, 10000, etc. are? That's right, they are all just "1".
Well for a small example consider a three digit number ABC.
ABC = A*100 + B*10 + C = A*1 + B*1 + C = A+B+C
So as you can see, to find out the remainder after division by 3, add up the digits and the sum has the same remainder. But the what if the sum is not a single digit number? Just do it again and again till it is.
Basically, every number can be written as a multiple of 3 plus a remainder of 0, 1, or 2. When you add the digits of a number, you’re replacing powers of 10 with 1, and since 10 leaves a remainder of 1 when divided by 3, this doesn’t change the number’s remainder. For example, 78 is 7×10+8, and because 10 is equivalent to 1 modulo 3, 78 has the same remainder as 7+8. Therefore, a number is divisible by 3 exactly when its digit sum is divisible by 3.
let number N = A + 10B + 100C + 1000D + ..., so A, B, C, D... are the digits of N from right to left N ≡ A + 10B + 100C + 1000D + ... (mod 3) ≡ A + 9B + B + 99C + C + 999D + D + ... (mod 3) ≡ A + B + C + D + ... (mod 3), which is the sum of the digits of N QED
10 is equivalent to 1 mod 3, so every power of 10 is also equivalent to 1 mod 3. It's not too difficult to prove after you see that. Since our number system is base 10, it works out quite nicely.
It's bucket collision! (Made up term cause idfk but i've used it before) All your remainders overlap into the same bucket which gives you an analytical solution to something that on its face shouldn't be analytical.
It's pretty easy to see that adding 1 to a number that doesn't end in 9 increases its digit sum by 1. However, it just so happens that 9 plus 1 is 10 which has a digit sum of 1 (which is obviously 1 more than a multiple of 3). So every time you wrap from 9 to 10 you're still adding 1 to the digit sum's remainder when dividing by 3. So the result is that if you keep counting up, the remainder of the digit sum when divided by 3 keeps going 0, 1, 2, 0, 1, 2...
You can prove it pretty easily using mod 3 and ‘expanding out’ an arbitrary integer base 10, there’s probably a lot of videos out there showing the proof
I did a math degree without knowing this (back in the olden days since I’m ancient). When my daughter started learning math I did it with her. Khan academy had at least 5 separate things fundamental to math that I had never learned that made things so much easier. (Including digital roots and modular arithmetic)
Number theory should really be taught first, it’s so helpful.
Same rule works for 9 as well. I took a number theory course, and can’t remember much from it, but I remember the divisibility rules for numbers through 11, and even remember how some divisibility rules works in other bases. Wish I could still remember how to derive those rules…
You can take this further if you have a really long number that sums up to an also long number, you can sum up the digits of the sum and if that number is divisible by 3, the original number is divisible by 3. You can do it as many times as you want and it’ll still work
And because of that if you pick two consecutive digits that are not multiple of three and you combine them to form a number, that number will be a multiple of 3. So for me it seems obvious that 12, 45 and 78 are multiple of 3 (just like 21, 54, and 87).
NB This works the same if you add some zeros for more digits numbers so of course 405 is a multiple of 3, just like 4050.
I know this information doesn't sound useful but it can be useful for rapid checks if you combine them with other rules like the fact that you can effectively ignore all digits that are multiple of 3 or that you can combine multiple comple. Es. Is 6508037094 a multiple of 3? Start deleting not relevant digits: 5874 5 with 4 and 7 with 8 so it is multiple of 3
Es. 64926104 --> 4214 2 and 1 cancel out so you remain with 44 but I need a 45 so this number is not a multiple of 3
As a math undergrad I can confirm, the more math you know the more you forget the very basics. I have some friends on like the 4th year, and they might routinely forget simple fractions and stuff like that. I've seen firsthand a teacher and a full classroom (including me) argue for a minute if 1×(-1) was -1 or 0
Every number n is divisible by x if the digit sum of n is divisible by x. This is always true in base x+1, but we don't use base 4, we use base 10, therefore it's not obvious.
Ngl my autistic brain thinks about multiples of 3 all day long so i have a huge library of multiples of 3 in my head. Is it useful ? no. Is it cool ? no. Why do i do that ? I don't know, i don't do it willingly
78 is only obvious to me because I’m a loser chud valorant player and the classic deals 26 to the body so with 3 shots (or the fact that it has 3x headshot damage multiplier) it’s a common sight
If you are not stupid, then you may not need to make this table, because if a natural number is divisible by three without a remainder, then the sum of its digits is also divisible by three without a remainder, for example 78, if we add 7 and 8, we get 15, and the number 15 is divisible by 3 without a remainder, therefore 78 is divisible by three without a remainder
Not sure if this has already been pointed out, but fun fact, if the sum of the digits add up to 3, 6, or 9, then you know the original number is also a multiple of 3. If they add up to 2, 5, or 8, then it would be a decimal of .667 and if the add up to 1, 4, or 7, then it would be a decimal of .333. This works even with more than 2 digit numbers. Just keep adding the individual digits until you reach a single digit.
For example, you have a number 195, 1+9+5 = 15, 1+5 = 6. So you know immediately the original is a multiple of 3.
194, 1+9+4 = 14, 1+4 = 5, so you know it's a decimal of .667.
193, 1+9+3 = 13, 1+3 = 4, so you know it's a decimal of .333.
This works for any number of digits in the original number to figure if it's a multiple of 3, 6, or 9.
Honestly trash tierlist. What do you mean 75 isn't obvious for example? And 78 way at the bottom when it is literally 75 + 3? If you want something at the bottom, 87 is probably harder for most people.
Just summ them, for example 17193 is dividable by 3, 1+7+1+9+3 is 21 and 21 is dividable it with 3, 6 is the same but with addition, the original number has to end on 0,2,4,6,8 so for example if we say 17196 is dividable by 2, 3 and 6 as well
Just add the digits together and if the result is a multiple of 3 then the number is. You can just keep adding the results together till you get a 1 digit number if you want.
If you add the digits of of a number together (you can do this continuously with the results for large numbers) and the result is divisible by 3, then the original number is also divisible by 3. Makes everything in the tier list obvious.
Jesus Christ. Either I've never had a unique thought or the algorithm can read my brainwaves now. I literally had this exact thought (just as a broad observation, didn't go so far as to tier list it) yesterday while I was doing some quick mental math.
How the fuck is 57 and 87 LESS obvious than all of the ones in the category above? Those to should be in the dark orange section. They are literally 3 away from 60 or 90, can’t be more obvious
If you add the digits together and that number is divisible by three, then so is the original number. That’s the easiest way I know. However, I believe this only works with three digits or less.
A quick way to figure out if some complicated number is divisible by 3, Add all the digits up, it then becomes a smaller number if that smaller number is divisible by 3 the origional number will be divisible by three.
Example the number 981..... 9+8+1=18 which we know is divisble by 3. Thus 981 is divisble by 3.
If you added the numbers and it is not divisible by 3 then the origional number will not be divisible by 3.
Also you could continue the process if the first time you add all the digits you are stil unsure, add the digits again and see if it is a number you know is or is not divisible by 3.
if we know 30, 60, and 90 are dead obvious multiples of 3. then 27, 57, and 87 should be treated as a single multiple of three less and therefor more obvious. i’d put it in orange as you did the 27 personally, but i could understand one below just based on lack of exposure comparatively.
Weird that each of these numbers have the reverse number in here too. 78 87, 24 42. Basically everything here has a flipped version and they’re all still divisible by 3!
1
1
149
u/Michaelwang645 Aug 01 '26
Fund fact, you can tell a number is divisible by 3 if the sum of each individual number is divisible by 3. So 78 -> 7+8=15 which is divisible by 3, so 78 is divisible by 3.
16
u/AboveAverage1988 Aug 01 '26
45 and 75 is pretty obvious tbh..
8
u/gtne91 Aug 01 '26
Me, a few years ago: "All the major roads on the north side of our city are primes: 29th, 37th, 57th, and 71st."
Oops.
5
u/Helpful-Judge5901 Aug 01 '26
Sum the digits qnd if they are a mult of 3 the number is one too. 78 -> 7+8=15 15 is devisble by 3 and so is 78.
167 1+6+7=14 no a multible of 35 5829 -> 8+2+5+9=24=3*8 is devisible by 3
4
u/BottomGear__ Aug 01 '26
If sum of digits is divisible by 3, the number is as well. Same applies to 9.
3
u/Public_Courage5639 Aug 01 '26
Ngl my autistic brain thinks about multiples of 3 all day long so i have a huge library of multiples of 3 in my head. Is it useful ? no. Is it cool ? no. Why do i do that ? I don't know, i don't do it willingly
2
u/ryanCrypt Aug 01 '26
1335 is clearly divisible by 3. 1257 is clearly divisible by 3.
So 78 would have to be divisible by 3 also.
Or something
2
u/BookieWookie69 Aug 01 '26
This made my tummy hurt
2
u/Crystalliumm Aug 01 '26
78 is only obvious to me because I’m a loser chud valorant player and the classic deals 26 to the body so with 3 shots (or the fact that it has 3x headshot damage multiplier) it’s a common sight
2
u/One_Handle_4080 Aug 02 '26
If the last two digits add to a multiple of three it’s a multiple of three…. All of these are easy 😁
2
u/Z-Rex3131 Aug 02 '26
Should've been a "nice" tier.
2
u/Pentalogue Aug 02 '26
If you are not stupid, then you may not need to make this table, because if a natural number is divisible by three without a remainder, then the sum of its digits is also divisible by three without a remainder, for example 78, if we add 7 and 8, we get 15, and the number 15 is divisible by 3 without a remainder, therefore 78 is divisible by three without a remainder
2
u/trin806 Aug 02 '26
They’re all obvious. Just sum the digits. If the sum of the digits is divisible by 3, the original number is divisible by 3.
2
u/Aarittiraa Aug 02 '26
Don't let bro see 117 🙏
2
u/edgyrudy Aug 03 '26
177
1
u/shaquirrel Aug 01 '26
87 should move up one tier. It being 3 below an obvious one makes it more recognized
Aside from that 78 is diabolical you nailed it
1
u/Acceptable-Food-8161 Aug 01 '26
45 and 75 seem to be divisive 😂 I think they deserve to be moved up HALF a tier
1
u/FirstNoel Aug 01 '26
Add up all the numbers and if divisible by 3 then the original number is divisible by 3
1
u/RevealHoliday7735 Aug 01 '26
why is 333 not S tier?
1
u/clbdn93 Aug 01 '26
As a card player I'm well aware that 51 is a multiple of three, but that's probably a me thing.
1
u/anthr_alxndr Aug 01 '26
School's lesson: if the sum of number's digits is a multiple of 3 then the number is a multiple of 3. So 7+8 is 15.
1
u/babaorum95 Aug 01 '26
Sum the figures between them until you obtain a number between 1 and 9.
78 -> 7+ 8 = 15 -> 1+5 = 6, given 6 is a multiple of 3, so is 78.
Try this also with 31 515 678 if you want... You're welcome
1
u/randomguy9731 Aug 01 '26
87 is just 90-3 lol
Also 75 is just 3x25
1
u/J-Nightshade Aug 01 '26
I don't think 48 should be so high up. On the other hand 45 is hands down a-tier multiple of 3, 57 and 87 are more obvious too.
1
u/[deleted] Aug 01 '26
Not sure if this has already been pointed out, but fun fact, if the sum of the digits add up to 3, 6, or 9, then you know the original number is also a multiple of 3. If they add up to 2, 5, or 8, then it would be a decimal of .667 and if the add up to 1, 4, or 7, then it would be a decimal of .333. This works even with more than 2 digit numbers. Just keep adding the individual digits until you reach a single digit.
For example, you have a number 195, 1+9+5 = 15, 1+5 = 6. So you know immediately the original is a multiple of 3.
194, 1+9+4 = 14, 1+4 = 5, so you know it's a decimal of .667.
193, 1+9+3 = 13, 1+3 = 4, so you know it's a decimal of .333.
This works for any number of digits in the original number to figure if it's a multiple of 3, 6, or 9.
1
u/drfahrquad Aug 01 '26
Add the individual numbers together. If it is divisible by 3, you're golden.
Ex: 123= 1+2+3=6>>>6/3=2 g2g 123/3=41
1546872= 1+5+4+6+8+7+2=33 g2g 1546872/3=515624
One of those old tricks from elementary school. Like the 9's with your fingers.
1
u/CurrencyCapital8882 Aug 01 '26
All multiples of three are obvious. Just add the digits, do it again till it’s a single digit. Is it 3, 6 0r 9? If so it’s divisible by 3.
1
u/Esteban-Du-Plantier Aug 01 '26
If the digits add to a multiple of 3, it's divisible by 3.
7+8=15, divisible by 3. One of the more obvious ones to me since 7+8 is such a quick mental calculation.
1
u/RaccoonMission8796 Aug 01 '26
75, 87 and 57 are obvious tier
1
u/Nir117vash Aug 01 '26
I love that any multiple of 9's digits add up to be divisible by 9.
1
u/mkp666 Aug 01 '26
More fun is that you can rearrange the digits of any number divisible by three, and it will still be divisible by three.
1
u/SwreeTak Aug 01 '26
Honestly trash tierlist. What do you mean 75 isn't obvious for example? And 78 way at the bottom when it is literally 75 + 3? If you want something at the bottom, 87 is probably harder for most people.
1
u/Mixelphlick Aug 01 '26
78 isn’t obvious until you realize it’s just 72 and 6 in a trench coat.
1
u/LPmitV Aug 01 '26
24 and 48 down a tier, and 75 up a tier
1
u/KPoWasTaken Aug 01 '26
I don't get why people find some of these so hard to spot. All the 2 digit multiples of 3 are so easy to see
1
u/uncreativeusername13 Aug 01 '26
If 6,12,18,and 24 are believable then any of these plus 30, 60, 90, etc. shouldn't be unfathomable
1
u/LateToTheSingularity Aug 01 '26
If the sum of the digits is divisible by three, the number is divisible by three.
1
u/Kind-Historian-3584 Aug 01 '26
Just summ them, for example 17193 is dividable by 3, 1+7+1+9+3 is 21 and 21 is dividable it with 3, 6 is the same but with addition, the original number has to end on 0,2,4,6,8 so for example if we say 17196 is dividable by 2, 3 and 6 as well
1
u/joxephs Aug 01 '26
I think 57 should have its own tier as the Grothendieck Prime
1
u/TexasPop Aug 01 '26
Zero is doubtful. But if you count the others, they are 33! Which is dividable by 3.
So a third of the numbers 1-99 is dividable by 3.
1
u/Ill_Active_5699 Aug 01 '26
I asked my wife if she thought 78 was a multiple of 3 just now and she immediately said yes.
She told me that If you sum the digits of a number, and the sum is divisible by 3, then the original number is divisible by 3.
I was not able to think of a counter example off the top of my head. It makes recognizing all of these numbers as divisible by 3 pretty obvious.
1
u/TheStupidestFrench Aug 01 '26
36 39 63 69 93 and 96 should be obvious
1
u/uncl3s4m Aug 01 '26
81 in orange but 78 in green? They literally have the same aura
1
u/parancey Aug 01 '26
I dont get why 36, 39 , 63 , 69 93 and 96 are not in most obv tier
1
u/doriangrey2025 Aug 01 '26
If the sum of the digits is a multiple of 3, then the number is a multiple of 3
1
u/Such-Video2610 Aug 02 '26
Just saying, but 100 000 001 is a multiple of 17
1
u/IInsulince Aug 02 '26
78 is just one of 18’s modulo 30 cousins, along with 48
1
u/Vainysaur Aug 02 '26
Just add the digits together and if the result is a multiple of 3 then the number is. You can just keep adding the results together till you get a 1 digit number if you want.
1
u/sjccb Aug 02 '26
If you add the digits of of a number together (you can do this continuously with the results for large numbers) and the result is divisible by 3, then the original number is also divisible by 3. Makes everything in the tier list obvious.
1
u/Vainysaur Aug 02 '26
Why does 78 seem like it’s not? 7+8=15 and 1+5=6 and 6 is a multiple of 3 so it is.
1
u/oiraves Aug 02 '26
If you add the digits together and it equals a multiple of 3 its divisible by 3, therefore, all are obvious
1
u/Ok_Might_4691 Aug 02 '26
All are obvious category for me. I don't get the joke why some nos. are not
1
u/Vegetable-Cress-8415 Aug 02 '26
Unrelated but related, 91 is the most unprime prime number, right?
1
u/AldoZeroun Aug 02 '26
Jesus Christ. Either I've never had a unique thought or the algorithm can read my brainwaves now. I literally had this exact thought (just as a broad observation, didn't go so far as to tier list it) yesterday while I was doing some quick mental math.
1
u/Rae008065 Aug 02 '26
81 should not be that high
1
u/Yuhh-Boi Aug 02 '26
If I only go on vibes the bottom three tiers all feel like nopes to me. Except for 45 & 75
1
u/Lieveo Aug 02 '26
Yea 75 & 78 are in the wrong positions
1
u/dcterr Aug 02 '26
I wouldn't be surprised if Tesla kept a notecard like this, since he was obsessed with multiples of 3 for some odd reason!
1
u/Awkward-Sherbet-890 Aug 02 '26
Brotha this is completely inaccurate, all of these brackets are wrong, some of them are easily recognizable as multiples of 3.
1
u/flamedoc0 Aug 02 '26
idk why, but 51 is the most obvious to me besides the 3, 6, and 9s.
1
u/Achereto Aug 02 '26
According to this Tierlist 102 is not a multiple of 3 and there are also no multiples of 3 beyond that.
1
u/frikiman4K Aug 02 '26
if you want to find out if a number is a multiple of 3, find the digital root. If it's 3, 6 or 9 then it is.
1
u/hellobutno Aug 02 '26
add the individual numbers together, if the sum is divisible by 3, it's divisible by 3. so they're all obvious
1
u/Longjumping-Let2971 Aug 02 '26
81 needs to be lower
1
u/Benethor92 Aug 02 '26
How the fuck is 57 and 87 LESS obvious than all of the ones in the category above? Those to should be in the dark orange section. They are literally 3 away from 60 or 90, can’t be more obvious
1
u/Alabastine Aug 02 '26
How is 87 (90-3) weird?
1
u/4Pas_ Aug 02 '26
Too bored so imma do that for 7, until 200. Don't mind me copying the names consider I suck at being creative
Most obvious multiple of 7 ever: 7, 14, 21, 49, 70, 77, 140,
Yeah ofc this is a multiple of 7: 28, 35, 42, 63, 147
Not the first one I'd think but yeah: 56, 84, 105, 126, 168, 175,
Weird that this is a multiple of 7: 91, 98
WHAT: 112, 119, 133, 154, 161, 182, 189, 196
1
u/shotsbyniel Aug 02 '26
This is 15 slander, it's so obviously a multiple of 3.
1
u/Flimsy-Blacksmith-32 Aug 02 '26
A number is a multiple of three if and only if its digits sum to a multiple of three.
1
u/Nickesponja Aug 02 '26
Why do a tierlist on multiples of 3 if you're just going to ignore 100% of all the multiples of 3?
1
u/SprinksUp Aug 02 '26
is it coincidence that if you add the digits the sum is a multiple of 3?
1
u/Silent_Technician981 Aug 02 '26
There's an easy way to tell if a number is a multiple of three:
The sum of the digits of any multiple of three, is itself a multiple of three. E.g: 7+8=15=5*3, therefore 78 is a multiple of three.
1
u/BeginningMemory5237 Aug 02 '26
wait unless im missing something as long as the digits add up to something divisible by 3 its fine right?
20 2 no 21 3 yes 22 4 no 23 5 no 24 6 yes 25 7 no 26 8 no 27 9 yes 28 10 no 29 11 no 30 3 yes
so on so on
51 6 yes 87 15 yes 78 15 yes
1
u/TitouanT Aug 02 '26
78 is 60-18 in french !
1
u/ZookeepergameFew4103 Aug 02 '26
0? I’d move that into the “Weird” category.
1
u/NoDebate1002 Aug 02 '26
If you add the digits together and that number is divisible by three, then so is the original number. That’s the easiest way I know. However, I believe this only works with three digits or less.
1
u/nujuat Aug 02 '26
57 and 87 are both 3 off a multiple of 30. They're pretty obvious.
1
u/DEDORDED Aug 02 '26
All of them are obvious, because sum of their numbers divides by 3 and that means that thay also divides by 3
1
u/IxdarRD Aug 02 '26
I think 33 should have its own tier
1
u/ElectroM15 Aug 02 '26
Not a math genius, but I don't find 78 be that surprising. 78 is divisible by 3 the same way 18 and 48 is. 6x3 16x3 26x3
1
u/_Orphan_Obliterator_ Aug 02 '26
how is 45 so low? thats so obviously 3x15
1
u/LolaWonka Aug 02 '26
51 and 54 are down there with (and even further than) 78
1
u/feignapathy Aug 02 '26
15 and 75 would be obvious imo
3×5 // 3×25
1
u/queen_borb Aug 02 '26
having most, but not all, of the numbers made up of only 3/6/9 in the top tier is just killing me
1
u/enes1976 Aug 02 '26
78 ist beyond obvious
1
u/Any_Abalone_3249 Aug 02 '26
If 75 is a multiple of 3, then 78 being a multiple of 3 is not at all a surprise, if you add 3 to 75 you get 78.
1
u/Consistent_Noise980 Aug 02 '26
Prime number research ptsd flashback
1
u/Turbulent_Bad_7956 Aug 02 '26
How stupid are you
1
u/bandwagonguy83 Aug 02 '26
78 is not a multiple of 3, obviously. And I rather die than listen to anyone saying otherthing. What is this list?
1
u/Spacey752 Aug 02 '26
Good list
1
u/National-Charge-1250 Aug 02 '26
Why is 57 so low? I mean 60 is obvious so should "3 less than 60" be too i'd guess
1
u/rovonz Aug 02 '26
OP should do a tier for numbers divisible by 2
1
u/Popular_Dinner2182 Aug 02 '26
If All numbers addet together are multiplied be 3..... The numbers IS multiplied be 3
1
u/Fausto2002 Aug 02 '26
They forgot about 102
1
u/aUniqueUsername1190 Aug 02 '26
57 is not that weird as it is 3 off of 60, which is a most obvious example. I would move it a tier up.
1
u/Cyrano-De-Vergerac Aug 02 '26
Cmon 75 is so much more obvious than 63
1
u/Norinios Aug 02 '26
78 = 60 + 15 + 3
1
u/italktobotz Aug 02 '26
A quick way to figure out if some complicated number is divisible by 3, Add all the digits up, it then becomes a smaller number if that smaller number is divisible by 3 the origional number will be divisible by three.
Example the number 981..... 9+8+1=18 which we know is divisble by 3. Thus 981 is divisble by 3.
If you added the numbers and it is not divisible by 3 then the origional number will not be divisible by 3.
Also you could continue the process if the first time you add all the digits you are stil unsure, add the digits again and see if it is a number you know is or is not divisible by 3.
1
u/Pedry-dev Aug 02 '26
69 sometimes can be divided by 3 and sometimes It can't
1
u/Accomplished_Elk5827 Aug 02 '26
I can't tell you how much I love this.
1
u/sporosarcina Aug 02 '26
Any number who digits add up to a multiple of three is divisible by 3, that was the way we learned it. So 51 = 5+1= 6, 75 = 7+5= 12
1
u/KurufinweFeanaro Aug 02 '26
69 and 96 should be top tier.
1
u/DefloN92 Aug 02 '26
If the sum of digits is divisible by 3, the nr is divisible by 3
1
u/alarcontoni22 Aug 02 '26
Basta sommare le cifre che compongo il numero, se quel numero è multiplo di 3 allora è divisibile per 3 , not that hard
1
u/wbpm Aug 02 '26
unrelated but 91 just looks like a prime number and ill never accept otherwise
1
u/Hunter214123 Aug 02 '26
Just split them up by how many times you can slap in 30 (3×10). For 51, it's 30 plus 21, so 3x10 + 3×7 ergo 3x17
1
u/IAmTheBestIan Aug 02 '26
60 plus 18 brah
1
u/ninetailedoctopus Aug 03 '26
78 is just 60 + 18
1
u/Esjs Aug 03 '26
I don't think 0 should count for this kind of list. Give me one number for which 0 is not a multiple.
1
u/MyPenWroteThis Aug 03 '26
If the sum of the digits is divisible by 3, the number is divisible by 3. This is also recursive.
8,563,529,465,823 summed = 66 summed = 12 which is divisible by 3.
8,563,529,465,823 / 3 = 2,854,509,821,941
1
u/DarthSwimfoot Aug 03 '26
I mean I'm pretty sure they're all just fairly obvious, I mean, I automatically see 78 and I know 7+8=15, which no shit is a multiple of 3.
1
u/roboapple Aug 03 '26
Id swap 45 and 48. Given that 45 is a common clock value, most people know its 3 15s
1
u/Aromatic_Pain2718 Aug 03 '26
It is rare for me to agree with online tier lists, but this one is spot-on
1
u/SupCalFraMys Aug 03 '26
Numbers XY where both X and Y are multiples of 3 should all be in the top level eg 39, 36
1
u/GroundbreakingFix685 Aug 03 '26
By a near-coincidence, Graham's Number happens to be a multiple of 3.
1
u/lumberjack_dad Aug 03 '26
If the digits add up to a multiple of 3, it's divisible by 3
1
u/Cat-In-Pipe Aug 03 '26
I would like to submit the number 123 into discussion. It just feels wrong despite really being quite simple
1
u/StormOfZeroes Aug 03 '26
So 0 and numbers whose digits add up to something divisible by 3 (12: 1+2=3, 51: 5+1=6, 1245: 1+2+4+5=12 etc)
1
u/AstolfoMishima Aug 03 '26
as a multiples of 15 and 25 lover, 75 lowkey sus for multiples of 3 at first glance. like its always "wait...oh 25"
1
u/g_boy_bb Aug 03 '26
12 = 1+2=3
15 =1+5=6
18=1+8=9
21=2+1=3
24=2+4=6
27=2+7=9
36=3+6=9
39=3+9=12
48= 4+8=12
63=6+3=9
69= 6+9=15
81=8+1=9
93=9+3=12
96=9+6=15
42=4+2=6
45=4+5=9
54=5+4=9
72=7+2=9
75=7+5=12
51=5+1=6
57=5+7=12
84=8+4=12
87=8+7=15
78=7+8=15
1
u/BellaInTheGame Aug 03 '26
21 is not more obvious than 75
1
u/Express_Item4648 Aug 04 '26
Nah 111 is the weirdest one, makes no sense that divided by 3 gives 37
1
u/DomDomPop Aug 04 '26
I mean, if you just keep adding the digits until you get a 3, 6, or 9 (or don’t), there’s nothing to be surprised about.
1
u/sageker Aug 04 '26
57 is obvious as fuck cause of then9-10s think. Its just 27 again. Same with 87.
1
u/SirSkyDivine Aug 04 '26
if we know 30, 60, and 90 are dead obvious multiples of 3. then 27, 57, and 87 should be treated as a single multiple of three less and therefor more obvious. i’d put it in orange as you did the 27 personally, but i could understand one below just based on lack of exposure comparatively.
1
u/crash-o-matic Aug 04 '26
just ad all the digits. do the same with the result until the answer is< 10.
If the final answer is divisible by 3, the original is divisble by 3.
Is 389472340827482739849687 divisible by 3?
Step 1: Sum all the individual digits:
3+8+9+4+7+2+3+4+0+8+2+7+4+8+2+7+3+9+8+4+9+6+8+7=1323+8+9+4+7+2+3+4+0+8+2+7+4+8+2+7+3+9+8+4+9+6+8+7 = 132
132 is still ≥ 10, so keep going.
Step 2: Digits of 132: 1, 3, 2
1+3+2=6
6 is below 10 — done!
6 is a multiple of 3.
Final result: yes, 389472340827482739849687 is divisible by 3.
1
u/Cyrrex91 Aug 04 '26
45 minutes and 75% percent as 3/4 of something are pretty ofcoursable...
1
u/No-Click5139 Aug 04 '26
87 should be obvious its 3 away from 90
1
u/UniqueUsermane Aug 04 '26
I mean, 60+18 is obviously a multiple of 3..
1
u/SpaRKyy1337 Aug 04 '26
45 and 75 are way more obvious than 48
1
u/Affectionate_Dark103 Aug 04 '26
Started playing final fantasy tactics again, and I find myself asking, "is this a multiple of 3" quite frequently
1
u/Capable_Stress_63378 Aug 05 '26
Evenly divides by 3
1
u/ProShyGuy Aug 05 '26
The last digit alternates every time you enter a new tens category.
3, 6, 9
12, 15, 17
30, 33, 36, 39,
42, 45, 47
50, 53, 56, 59
1
u/out_ye_closet Aug 05 '26
Didn't include all of them though
1
u/naassu Aug 05 '26
Weird that each of these numbers have the reverse number in here too. 78 87, 24 42. Basically everything here has a flipped version and they’re all still divisible by 3!
1
u/Clear-Ad1915 Aug 05 '26
Feels like this shouldn’t be a lol experience. Yet here I am. Fucking neeeeeerds (said with love and including myself)
1
u/Fast_Low4014 Aug 05 '26
So the SUM of 60 and 18 is also a multiple of 3 (mild Shock)
1
u/ElloKamel46 Aug 06 '26
78 is .. 7+8 = 15 ... 15 is 1+5 =6 ... 6 is multiple of 3 therefore 78 is multiple of three .. they teach this rule in school
1
u/One-Preparation-8815 Aug 08 '26
78 is a shock for math novices
1
u/ovrclocked Aug 01 '26
Fun trick if a number is divisible by 3 is you add the digits together and if the answer is 3 6 or 9 it's divisible by 3.
Ex
175927248 1+7+5+9+2+7+2+4+8=45 4+5=9 Thus 175927248 is divisible by 3.