Divisibility Rules

Dividing by 3
Add up the digits: if the sum is divisible by three, then the number is as well. Examples:
111111: the digits add to 6 so the whole number is divisible by three.
87687687. The digits add up to 57, which is divisible by three. If you didn't know that, you could work out that 5+7=12 which 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:
3. 100 is divisible by 4 because 00 is divisible by 4.
4. 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.

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.
How can you tell whether the last three digits are divisible by 8?
If the first digit is even, the number is divisible by 8 if the last two digits are. If the first digit is odd, subtract 4 from the last two digits; the number will be divisible by 8 if the resulting last two digits are. So, to continue the last example, 33333888 is divisible by 8 because the digit in the hundreds place is an even number, and the last two digits are 88, which is divisible by 8. 33333886 is not divisible by 8 because the digit in the hundreds place is an even number, but the last two digits are 86, which is not divisible by 8.

Dividing by 9
Add the digits. If they are divisible by nine, then the number is as well. This holds for any power of three.

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

Dividing by 11
Here's an easy method.
Take any number, such as 365167484.
Add the first, third, fifth, seventh,.., digits.....3 + 5 + 6 + 4 + 4 = 22
Add the second, fourth, sixth, eighth,.., digits.....6 + 1 + 7 + 8 = 22
If the difference between the two numbers is divisible by 11 (0 is divisible by 11), then so is the number.
22 - 22 = 0 so 365167484 is evenly divisible by 11.

Dividing by 12
Check for divisibility by 3 and 4.

Dividing by 13
Kill the last digit from the given number. Then subtract nine times the deleted digit from the remaining number. If what is left is divisible by 13, then so is the original number. If you don’t know if the remaining number is divisible by 13 or not, apply the rule again.
Example: We want to find out whether 403 is divisible by 13. Remove the last digit (3), and subtract 27 from the rest of the number. We get 13, which is divisible by 13, so 403 divides 13.

Dividing by 14
A number is divisible by 14 if and only if it is an even number and divisible by 7.

This information was copied and edited from:
http://mathforum.org/k12/mathtips/division.tips.html