DIVISIBILITY RULES
2
If the last digit is even, the number is divisible by 2.
Example: 3514: 4 is even, so 3514 is divisible by 2
If the sum of the digits is divisible by 3, the number is also.
3
Examples:
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.
If the last two digits form a number divisible by 4, the number is also.
4
5
Examples:
1. 100 is divisible by 4.
2. 1732782989264864826421834612 is divisible by four also, because
12 is divisible by four.
If the last digit is a 5 or a 0, the number is divisible by 5.
Example: 4135: It ends in a 5, so it is divisible by 5
If the number is divisible by both 3 and 2, it is also divisible by 6.
6
Example: 5334: 5 + 3 + 3 + 4 = 15, which is divisible by 3, so 5334 is too
4 is even, so 5334 is divisible by 2
Since it’s divisible by 3 AND 2, it is divisible by 6
Take the last digit, double it, and subtract it from the rest of the number;
if the answer is divisible by 7 (including 0), then the number is also.
7
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.
- this rule is a pain, but it does work…..
8 If the last three digits form a number divisible by 8, then so is the whole number.
Example: 33333888 is divisible by 8; 33333886 isn't.
If the sum of the digits is divisible by 9, the number is also.
9
10
Example: 82530: 8 + 2 + 5 + 3 + 0 = 18, which is divisible by 9,
So 82530 is also divisible by 9
If the number ends in 0, it is divisible by 10.
Example: 9,874,263,480: It ends in 0, so it’s divisible by 10
Add every other digit; Add digits not added before; Subtract those answers;
If that results in 0 or something divisible by 11 (22, 33, 44, etc.), the original number is
11 divisible by 11.
Example: 14652: 1 + 6 + 2 = 9, 2 + 5 = 9, 9 – 9 = 0,
So, 14652 is divisible by 11.