## 28 Jun 2018

### Rules of Divisibility (Divisibility Rule for 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11) with Examples

In this Post we will discuss Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 in detail with the help of examples. So go through this post to clear all your concepts about rules of divisibility

## Divisibility Rule for 2

A number is divisible by 2 when the digit at ones place is 0, 2, 4, 6 or 8.
For example- 12, 16, 286, 340 etc. are divisible by 2.

## Divisibility Rule for 3

A number is said to be divisible by 3, when the sum of its digits is divisible by 3.
For example- 210, 156 etc. are divisible by 3, because sum of digits of both of these numbers is divisible by 3.
2 + 1 + 0= 3, which is divisible by 3
Similarly, 1 + 5 + 6 = 12, which is also divisible by 3.
So here we see that sum of digits of the number is divisible by 3 therefore the whole number is divisible by 3.

## Divisibility Rules for 4

A number is divisible by 4, if the number formed with it's last two digits is divisible by 4.
For example- 18232 is divisible by 4, because the last two digits of this number i.e. 32 is divisible by 4. Therefore the whole number, 18232 is divisible by 4.

## Divisibility by 5

A number is said to be divisible by 5, when the digit at ones place is either 0 or 5.
For example- 150, 31820, 34355 are all divisible by 5, because these numbers have 0, 0 and 5 respectively at their units places.
But Numbers such as 124, 386, 259 are not divisible by 5.

## Divisibility Rule for 6

A number is divisible by 6, if it is divisible by both 2 and 3.
Example- 948 is divisible by 6, as it is divisible by both 2 (at units place it has 8) and 3 (9 + 4 + 8= 21, which is divisible by 3)
But the number 35378 is not divisible by 6, since it is divisible by 2 but not divisible by 3.

A number is divisible by 7, when the difference between twice the digit at ones place, and the number formed by the remaining digits is either 0 or a number divisible by 7. Let's understand the divisibility rule of 7 with an example-
Example- 658 is divisible by 7 because, 65-(2x8)=65-16= 49 is divisible by 7. Therefore this number is divisible by 7.

## Divisibility Rule for 8

A number is divisible by 8, only when the number formed by its last three digits is divisible by 8.
For example- 71720 is divisible by 8 because last three digits of this number i.e. 720, is divisible by 8. therefore this number is divisible by 8.

## Divisibility Rule for 9

A number is divisible by 9, if the sum of its digits is divisible by 9. Remember, this rule is similar to the rule of divisibility by 3. Let's take an example to understand the divisibility by 9.
Example- 525834 is divisible by 9 because 5 + 2 + 5 + 8 + 3 + 4 = 27, which is divisible by 9, so the number 525834 is divisible by 9.

## Divisibility Rule for 10

A number is divisible by 10 when the digit at it's units place is 0
For example- 1280 is divisible by 10, as the number at units place is 0.

## Divisibility Rule of 11

A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11. Here we will understand the divisibility rule of 11 with an example-
Example- 30426 is divisible by 11 as (3 + 4 + 6) - (0 + 2) = 11, which is divisible by 11. Therefore this number is divisible by 11.

## Important:

If a number is divisible by two numbers A and B, where A and B are co-primes, then the number is divisible by AB.