Math Made Easy: Divisibility Rules

Basic divisibility rules of numbers.

Can you still recall what your primary teacher taught you about divisibility rules of numbers? If your answer is no, then here’s an easy refresher course about the subject matter.

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If a number can be divided exactly by another number without any remainder, then we say:

The first number is divisible by the second and the second number divides the first.

1. Divisibility by 2

Even numbers with units digit of 0, 2, 4, 6, or 8 are divisible by 2.

2. Divisibility by 3

A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

Example: 8,247 is divisible by 3 because 8 + 2 + 4 + 7 = 21, and 21 is divisible by 3.

3. Divisibility by 4

If the last two digits of a number form a number that is divisible by 4, then the number is divisible by 4.

Note: Any number whose last two digits is 00 is considered to be divisible by 4.

Example 924: The last two digits in this number (2 and 4) is divisible by 4, so 924 is divisible by 4.

4. Divisibility by 5

If the last digit or units of a number is 0 or 5, then the number is divisible by 5.

5. Divisibility by 6

A number is divisible by 6 if the number is divisible by both 2 and 3. Or, any even number divisible by 3 is also divisible by 6.

6. Divisibility by 8

A number is divisible by 8 if the number formed by the last 3 digits is divisible by 8.

Example: 5,280 is divisible by 8 since the last 3 digits of the number (280) is divisible by 8.

7. Divisibility by 9

A number is divisible by 9 if the sum of the digits is divisible by 9.

Example: 1,545 is divisible by 9 since 1 + 5 +4 + 5 = 18, and 18 is divisible by 9.

8. Divisibility by 10

A number is divisible by 10 if the last digit or units digit is 0.

9. Divisibility by 11

A number is divisible by 11 if the difference between the sums of the digits in the odd places and the digits in the even places is either 0 or a multiple of 11.

Example: 8,591,726 is divisible by 11 since 8 + 9 + 7 + 6 = 30 and 5 + 1 + 2 = 8 30 – 8 = 22 (a multiple of 11).