Check out the divisibility rules below.

Dividing by 3

Add up the digits: if the sum is divisible by three, then the number is as well. Examples:

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  1. 111111: the digits add to 6 so the whole number is divisible by three.
  2. 87687687. The digits add up to 57, and 5 plus seven is 12, so the original number is divisible by three.

Dividing by 4

Look at the last two digits. If the number formed by its last two digits is divisible by 4, the original number is as well.
Examples:

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  1. 100 is divisible by 4.
  2. 1732782989264864826421834612 is divisible by four also, because 12 is divisible by four.

Dividing by 5

If the last digit is a five or a zero, then the number is divisible by 5.

Dividing by 6

Check 3 and 2. If the number is divisible by both 3 and 2, it is divisible by 6 as well.

Robert Rusher writes in:

Another easy way to tell if a [multi-digit] number is divisible by six . . .

is to look at its [ones digit]: if it is even, and the sum of the [digits] is

a multiple of 3, then the number is divisible by 6.

Dividing by 7

To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number.
Example: If you had 203, you would double the last digit to get six, and subtract that from 20 to get 14. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again.

 

Dividing by 8

Check the last three digits. Since 1000 is divisible by 8, if the last three digits of a number are divisible by 8, then so is the whole number.
Example: 33333888 is divisible by 8; 33333886 isn't.

 

Dividing by 9

Add the digits. If that sum is divisible by nine, then the original number is as well.

Dividing by 10

If the number ends in 0, it is divisible by 10.

Dividing by 12

Check for divisibility by 3 and 4.