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3	Kevin114514	3655
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9	BledDest	132
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Divisibility Rules for different divisors

For Divisor = 1

There is no specific condition. Every number is divisible by 1.

For Divisor = 2

If the last digit of the number is even, then that number is divisible by 2. For example, 0, 2, 4, 6, 8.

For Divisor = 3

The sum of the digits is divisible by 3, then that number is also divisible by 3.
Subtract the quantity of the digits 2, 5 & 8 from the quantity of the digits 1, 4, & 7. If this difference is divisible by 3, then that number is also divisible by 3. For Example, 16,499,205,854,376 has four of the digits 1, 4 and 7 and four of the digits 2, 5 and 8; since 4 − 4 = 0 is a multiple of 3, the number 16,499,205,854,376 is divisible by 3.
Subtracting the last digit of the number twice from the rest of the number. If this difference is divisible by 3, then that number is also divisible by 3. _ For Example, 405: 40 − 5 × 2 = 40 − 10 = 30 = 3 × 10._

For Divisor = 4

The last two digits form a number and that number is divisible by 4.
If the tens digit is even, the ones digit must be 0, 4, or 8.
If the tens digit is odd, the ones digit must be 2 or 6.
The sum of the ones digit and double the tens digit is divisible by 4.

Comments (4)

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acoder31415

4 months ago, hide # |

there's good divisibility rules up to like 20 btw

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wrusb

Divisibility rules for numbers 1−30

kaislash

a number n is divisible by m if n%m==0you don't need all that dawg

KnownAsJason

Metacommentary: for the one about three, as kaislash said n%m == 0 is probably a better test in nearly all cases (n < 1e18) since in checking for each digit of n is sum of mult of 3 will firstly still take o(logn) (each digit) time to get the sum but then you also have to recursively figure out if that sum is also a multiple of three which technically works but seems like implement hell. For divisor 4 i guess you could just do (n%100) (to get last 2 digits) then (n%100)%4 == 4 but at that point just do n%4 and atp i think its starting to become clear that using n%x==0 where x is the number testing for division is probably best. Interestingly, there are rules up to like a thousand or so somewhere on the depths of internet if you are really interested in that sort of thing.