# Number System - Divisibility Test of Numbers

### In this post, we will see " Divisibility Test of Numbers ".

divisibility test is a shortcut method of find out whether a given integer is divisible by a fixed number without performing the division, usually by examining its digits.

#### Divisibility of 2

The numbers whose unit's digit consists of 0, 2, 4, 6 and 8, then the required number is divisible by 2.

For example, in 2458 where the unit's digit is 8 and hence the number 2458 is divisible by 2

#### Divisibility of 3

If the sum of all digits in a number is divisible by 3, then the required number is divisible by 3.

For example, 492 where the sum of digits is 4 + 9 + 2 = 15 and 15 is divisible by 3 and hence 492 is divisible by 3

#### Divisibility of 4

If the last two digits in a number is divisible by 4, then the required number is divisible by 4.

For example, in 3424 where the last two digits is 24 and 24 is divisible by 4 and hence 3424 is divisible by 4

#### Divisibility of 5

The number whose unit's digit consists of 0 and 5, then the required number is divisible by 5.

For example, 295 where the unit's digit is 5 and hence the number 295 is divisible by 5

#### Divisibility by 6

If a number is divisible by both 2 and 3 then the required number is also divisible by 6.

The number to be divisible by 6 must satisfy two conditions :
1. Unit's place of the digit in the number should be 0, 2, 4, 6 and 8
2. Sum of all digits in the number should be divisible by 3
For example 492 where unit's place digit of the required number is 2 and sum of all digits in the number is 15 which is divisible by 3 and hence 492 is divisible by 6

#### Divisibility by 8

A number is divisible by 8  if the number formed by the last three digits of the required number is divisible by 8.

For example, in 9120 where the last three digits are 120 which is divisible by 8 and hence the number 9120 is divisible by 8

#### Divisibility by 9

If the sum of all digits in a number is divisible by 9, then the required number is divisible by 9.

For example, 792 where the sum of digits is 7 + 9 + 2 = 18 and 18 is divisible by 9 and hence 792 is divisible by 9

#### Divisibility by 10

If the unit's place digit of any number consists of 0 then the required number is divisible by 10.

For example 2590 where unit's place digit is 0 and hence the number 2590 is divisible by 10

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