Divisibility Rules for division by: 2,3,4,5,6,7,8,9,10 and 12

1. numbers are divisible by 2 if
 • the last digit ends in an even number
example: 358 (8 ÷ 2=4) so 358 is divisible by 2.

2. numbers are divisible by 3 if
 • adding the digits of a number results in a number divisible by 3
example: 456 (4+5+6 = 15) 15÷3 = 5, 456 is divisible by 3.

3. numbers are divisible by 4 if
 • the number formed by the last two digits are evenly divisible by 4
example: 288 (88÷4 = 22) eighty-eight is divisible by 4.

4. numbers are divisible by 5 if
 • the number ends in 0 or 5
example: 3,450 ends in 0 so 3,450 is divisible by 5.

5. numbers are divisible by 6 if
 • the number is divisible by 2 and 3
  (use the rules for divisibility by 2 and 3)
example: 78 (78 ends in 8 so it is divisible by 2);
   (7 + 8 =15, so 78 is divisible by 3) so 78 is divisible by 6.

6. numbers are divisible by 7 if
 • take the last digit in a number
 • double, and subtract the last digit in your number from the
   rest of the digits
 • repeat the process for larger numbers
example: 357 (double the 7 to get 14. Subtract 14 from 35 to
   get 21 which is divisible by 7)

7.  numbers are divisible by 8 if
 • the last three digits are divisible by 8, so is the entire
   number.
example: 6,032 (the last three digits are divisible by 8) so the
   entire number is also divisible by 8.

8. numbers are divisible by 9 if
 • the sum of the digits are divisible by 9.
example: 2,826 (2+8+2+6 = 18) so 2,826 is divisible by 9.

9. numbers are divisible by 10 if
 • the number ends in 0 (in ones place)
example: 6,540 (6,540÷ 10 = 654) so 6,540 is divisible by 10.

10. numbers are divisible by 12 if
 • divisible by 3 and 4.
   (use the rules for divisibility by 3 and 4)
example: 8,256 (8+2+5+6 = 21, 21 is divisible by 3);(8,256,
   56 is divisible by 4) so 8,256 is divisible by 12.