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, 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: 100 is divisible by 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.

TEST Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5. Repeat this sequence as necessary .Add the products. If the sum is divisible by 7 - so is your number.Example: Is 2016 divisible by 7? 6(1) +1(3) + 0(2) + 2(6) = 21 . 21 is divisible by 7 and we can now say that 2016 is also divisible by 7.

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.

Example:  12348 is divisible by 9; as the sum is 18

Dividing by 10

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

Example: 20 , 345ABCV80

Dividing by 11

Find the sum of alternate numbers and if the differnce between those two numbers is zero or multiple of 11 then the number is divisible by 11.

Let's look at 352, which is divisible by 11;  the answer is 3+2 is 5 and 5 - 5 = 0

another way  to say this is that 35 -2 is 33.

Dividing by 12

Check for divisibility by 3 and 4.

Example:  936, it is divisible by both 3 and 4 and thus by 12.

Dividing by 13

Delete 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.

Example:  104
10 - 36 = -26, which is divisible by 13 so 104 is divisible by 13

Dividing by 17

How can you know if a number with three or more digits is divisible by the number fourteen?

Check if the last digit of the original number is odd or even. If the number is odd, then the number is not divisible by fourteen. If the number is even, then apply the Dividing by 17 The result of subtracting five times the last digit from the number with the last digit removed is divisible by 17. Example: 187: "18" - ("7" x 5) = -17 is divisible by 17

Dividing by 19

The result of adding twice the last digit to the number with the last digit removed is divisible by 19.

Example: 437: "43" + ("7"x2) = 57 is divisible by 19.

Dividing by 23

The result of adding seven times the last digit to the number with the last digit removed is divisible by 23.

Example: 598: "59"+("8" x 7)= 115 is divisible by 23. 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.