Divisibility Rules, deals with various concepts which are as under:-

- Divisibility Rule for 2
- Divisibility Rule for 3
- Divisibility Rule for 4
- Divisibility Rule for 5
- Divisibility Rule for 6
- Divisibility Rule for 8
- Divisibility Rule for 9
- Divisibility Rule for 10
- Divisibility Rule for 11

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**Divisibility Rules Examples**

**Divisibility Rule for 2**** :-**

A number is divisible by 2, if the digit at ones place of that number is divisible by 2 or digit at ones place is 0, 2, 4, 6, 8.

**For Example** –

Question –

Check whether 2396 is divisible by 2 ?

Solution –

In,2396

6 is at ones place

and 6 is divisible by 2

So,2396 is also divisible by 2

**Divisibility Rule for 3**** :-**

A number is divisible by 3, if the sum of all the digits of the numbers are divisible by 3.

**For Example** –

Question –

Check whether 23973 is divisible by 3 ?

Solution –

In, 23973

Sum of its digits = 2 + 3 + 9 + 7 + 3 = 24

and 24 is divisible by 3

So, 23973 is also divisible by 3.

**Divisibility Rule for 4**** :-**

A number is divisible by 4, if the number formed by last 2 digits of that number (ones and tens place) is divisible by 4.

**For Example** –

Question –

Check whether 23924 is divisible by 4 ?

Solution –

In, 23924

24 is the number formed by tens and ones place.

and 24 is divisible by 4.

therefore, 23924 is also divisible by 4.

**Divisibility Rule for 5**** :-**

A number is divisible by 5 if the digit at ones place is either “0” or” 5″.

**For Example** –

Question –

Check whether 23920 is divisible by 5 ?

Solution –

In, 23920

0 is the digit at ones place

So, 23920 is divisible by 5.

**Divisibility Rule for 6**** :-**

A number is divisible by 6, if it is divisible by both 2 and 3.

**For Example** –

Question –

Check whether 23724 is divisible by 6 ?

Solution –

Checking Divisibility for 2,

A number is divisible by 2, if the digits at ones place is divisible by 2 or digit at ones place is 0, 2, 4, 6, 8.

In, 23724

4 is at ones place

and 4 is divisible by 2

So, 23724 is also divisible by 2.

Checking Divisibility for 3,

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

In, 23724

Sum of digits = 2 + 3 + 7 + 2 + 4 = 18

and 18 is divisible by 3

So, 23724 is also divisible by 3.

Therefore, 23724 is divisible by 2 and 3

Hence, 23724 is also divisible by 6.

**Divisibility Rule for 8**** :-**

A number is divisible by 8, if the number formed by last 3 digits of that number (ones, tens and hundreds place) is divisible by 8.

**For Example** –

Question –

Check whether 950720 is divisible by 8 ?

Solution –

In, 950720

720 is the number formed by ones, tens, and hundreds place digits or the number formed by last 3 digits .

and 720 is divisible by 8.

Hence, 950720 is also divisible by 8.

**Divisibility Rule for 9**** :-**

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

**For Example** –

Question –

Check whether 24597 is divisible by 9 ?

Solution –

In 24597,

Sum of digits = 2 + 4 + 5 + 9 + 7 = 27

27 is divisible by 9

So, 24597 is also divisible by 9.

**Divisibility Rule for 10**** :-**

A number is divisible by 10 if the digit at ones place is 0.

**For Example** –

Question –

Check whether 23920 is divisible by 10 ?

Solution –

In 23920,

o is at ones place

So, 23920 is divisible by 10.

**Divisibility Rule for 11**** :-**

A number is divisible by 11 if the difference between the sum of the digits at odd place and the digits at even place is either 0 or divisible by 11.

**For Example** –

Question –

Check whether 73920 is divisible by 10 ?

Solution –

A number is divisible by 11 if the difference between the sum of the digits at odd place and the digits at even place is either 0 or divisible by 11.

In, the given number, 73920

Sum of the digits at even places:

2 + 3 = 5

Sum of the digits at odd places:

0 + 9 + 7 = 16

Difference between sum of digits at odd and even place = 16 – 5 = 11 ( Which is divisible by 11 )

Therefore, 73920 is also divisible by 11

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