# Divisibility rule

A divisibility rule, also referred to as a divisibility test, is a rule that can be used to determine whether one number is divisible by another. Generally, a number is divisible by another if the quotient is a whole number (i.e. there is no remainder).

There are also divisibility rules for testing whether a given number is divisible by specific integers. The divisibility rules for the integers 1-10 are included below. Divisibility rules exist for other integers as well, but in some cases, applying the divisibility rule may be more tedious than just performing the division problem to see if the remainder is 0.

## Divisibility by 1

All numbers are divisible by 1. No matter what the number is, dividing it by 1 will result in the same number.

## Divisibility by 2

If a number has an even number (0, 2, 4, 6, 8) in the ones place, 2 divides the number. For example, 2 divides 3,018 because 8 is an even number.

## Divisibility by 3

If 3 divides the sum of the digits of a number, 3 divides the number. For example, 3 divides 2,310 because the sum of 2, 3, 1, and 0 is 6, and 3 divides 6.

## Divisibility by 4

If 4 divides the last two digits of a number, 4 divides the number. For example, 4 divides 8,728 because 4 divides 28.

## Divisibility by 5

If a number has a 0 or a 5 in the ones place, 5 divides the number. For example, 5 divides both 385 and 400.

## Divisibility by 6

If both 2 and 3 divide a number, 6 also divides that number. For example, 6 divides 396 because both 2 and 3 divide 396.

## Divisibility by 7

If the result of subtracting two times the last digit in a number from the rest of the number, excluding the last digit, is divisible by 7, then the original number is divisible by 7. Using 7,196 as an example:

6 × 2 = 12

719 - 12 = 707

707 ÷ 7 = 101

Since 7 evenly divides 707, 7,196 is divisible by 7.

## Divisibility by 8

If the last 3 digits in a number are 0, the number is divisible by 8. If the last 3 digits are not 0, but the number formed by the last 3 digits of the original number is divisible by 8, then the original number is divisible by 8.

Using 50,496 as an example:

496 ÷ 8 = 62

Since 496 is divisible by 8, 50,496 is divisible by 8.

## Divisibility by 9

If 9 divides the sum of the digits of a number, 9 divides the number. For example, 9 divides 198,432 because 1 + 9 + 8 + 4 + 3 + 2 = 27, and 9 divides 27, so 9 divides 198,432.

## Divisibility by 10

If the last digit of a number is 0, then the number is divisible by 10. For example, 10 evenly divides 710.