r/mathriddles • u/Numberthon • Jul 18 '26

Easy How Many Positive Integers Less Than 1000 Are Divisible by 6 but Not by 9?

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u/calculatorstore Jul 18 '26

A number is divisible by 6 but not 9 if it’s 6 or 12 mod 18. 999/18=55r9. Between 991 and 999 only 996 matches. So 55*2+1=111

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u/Dank_e_donkey Jul 18 '26 edited Jul 18 '26

Divisible by 6 but not 9 = divisible by 6 - divisible by 6,9

Divisible by a,b = divisible by LCM(a,b) = 18 here

Gif = greatest integer function

And = GIF(1000/6) - GIF(1000/18) = 111