Characteristic of number 
Number divisible by: 
Last digit is even 
2 
The sum of the digits is divisible by 3 
3 
The last two digits form a number divisible by 4 
4 
The last digit is 0 or 5 
5 
The number is divisible by both 2 and 3. 
6 
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.
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. 
7 
Example: Check
to see if 203 is divisible by 7.
 double the last digit: 3 x 2 = 6
 subtract that from the rest of the number: 20  6 = 14.
 check to see if the difference is divisible by 7: 14 is divisible
by 7, therefore 203
is
also divisible
by 7.

The last three digits form a number divisible by
8 
8 
The sum of the digits is divisible by 9 
9 
The numeral ends in 0 
10 
The (sum of the odd numbered digits)  (sum
of the even numbered digits) is divisible by 11.
Example:
34871903
3+8+1+0=12
4+7+9+3=23
2312=11
Is divisible by 11 
11 
The number is divisible by both 3 and 4. 
12 
Delete the last digit from the number, then
subtract 9 times the deleted digit from the remaining number. If what is left is divisible
by 13, then so is the original number. 
13 
The last four digits form a number divisible by
16 
16 
TEST TIP: If a
number is divisible by two different prime numbers, then it is divisible by the products
of those two numbers. Since 36, is divisible by both 2 and 3, it is also divisible
by 6. 