Divisibility Test / Divisibility Rules

We can find out whether one number is divisible by another number by examining the digits of the number.

‘Divisible by’ means a number divides another number without leaving any remainder.

Divisibility Rules

These below rules will help us to know whether one number is divisible by another without much calculation.

Divisibility by 2

Every number that ends in even number i.e. 0,2,4,6 or 8 is divisible by 2.

Example: 26, 92, 104, 200, 398 etc.

Divisibility by 3

If the sum of the digits of the given number is divisible by 3, then the given number is also divisible by 3.

Example: 414

              Sum of the digits of 414 = 4 + 1+ 4 = 9

              9 is divisible by 3 (9 ÷ 3 = 3). So, 414 is also divisible by 3

Divisibility by 4

Given number is divisible by 4, if the number formed by last two digits of the given number is divisible by 4.

Example: 1324

The last two digit of the given number is 24.

24 ÷ 4 = 6 (24 is divisible by 4)

So, 1324 is divisible by 4

Divisibility by 5

Number that ends in 5 or 0 is divisible by 5.

Example: 165

Here last digit is 5. So, 165 is divisible by 5

Divisibility by 6

Given number is divisible by 6, if the given number is divisible by 2 as well as by 3.

Example: 168

Step1: Test of divisibility by 2.

           Number 168 ends in even number i.e. 8. So, 168 is divisible by 2

Step2: Test of divisibility by 3.

           Sum of the digit of the given number 168 = 1 + 6 + 8 = 15

           15 is divisible by 3. So, 168 is divisible by 3.

As 168 is divisible by 2 as well as by 3. So, 168 is divisible by 6.

Divisibility by 7

Double the last number of the given number and then subtract it from the rest of the number left in the given number. If the answer we get is either 0 or any number divisible by 7, then the given number is divisible by 7.

Example: 336

Step1: Double the last digit

          Here last digit is 6. Double of 6 is 12.

Step2: Subtract the answer from the rest of the number.

          Number left is 33. So, subtract 12 from 33.

          33 – 12 = 21

Step3: 21 is divisible by 7. So, 336 is divisible by 7

Divisibility by 8

A number is divisible by 8, if the number formed by its last three digits is also divisible by 8.

Example: 71816

Here last three digits is 816.

816 ÷ 8 = 102

As 816 is completely divisible by 8. So, 71816 is also divisible by 8.

Divisibility by 9

Given number is divisible by 9, if the sum of the all the digits of given number is divisible by 9.

Example: 2016

Sum of the digit = 2 + 0 + 1 + 6 = 9

9 is divisible by 9. So, 2016 is divisible by 9

Divisibility by 10

Any number that ends in 0 is divisible by 10.

Example: 3670

As number ends in 0.So, 3670 is divisible by 10.

Divisibility by 11

Starting from left add all the number on odd positions and add all the number on even positions. Then subtract the two results. If the resultant number is divisible by 11 or is equal to 0, then the given number is divisible by 11.

Example: 3729

Sum of odd positions = 3 + 2 = 5

Sum of even positions = 7 + 9 = 16

Subtract the two results, 16 – 5 = 11. As 11 is divisible by 11, so 3729 is divisible by 11.