### Divisibility rule for 6 – Video Explanation

**Problem 1 – Divisibility rule for 6**

Check whether 89676 is divisible by 6?

**a) Yes**

b) No

Solution:

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

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, 89676

6 is at one’s place

and 6 is divisible by 2

So, 89676 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, 89676

Sum of its digits = 8 + 9 + 6 + 7 + 6 = 36

and 36 is divisible by 3

So, 89676 is also divisible by 3

Therefore, 89676 is divisible by 2 and 3

Hence, 89676 is also divisible by 6

**Problem 2 – Divisibility rule for 6**

Check whether 29402 is divisible by 6?

a) Yes

**b) No**

Solution:

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

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, 29402

2 is at one’s place

and 2 is divisible by 2

So, 29402 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, 29402

Sum of its digits = 2 + 9 + 4 + 0 + 2 = 17

and 17 is not divisible by 3

So, 29402 is not divisible by 3

Therefore, 29402 is divisible by 2 but not divisible by 3

Hence, 29402 is not divisible by 6

**Problem 3 – Divisibility rule for 6**

Check whether 64312 is divisible by 6?

a) Yes

**b) No**

Solution:

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

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, 64312

2 is at one’s place

and 2 is divisible by 2

So, 64312 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, 64312

Sum of its digits = 6 + 4 + 3 + 1 + 2 = 16

and 16 is not divisible by 3

So, 64312 is not divisible by 3

Therefore, 64312 is divisible by 2 but not divisible by 3

Hence, 64312 is not divisible by 6

**Problem 4 – Divisibility rule for 6**

Check whether 47283 is divisible by 6?

a) Yes

**b) No**

Solution:

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

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, 47283

3 is at one’s place

and 3 is not divisible by 2

So, 47283 is not 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, 47283

Sum of its digits = 4 + 7 + 2 + 8 + 3 = 24

and 24 is divisible by 3

So, 47283 is divisible by 3

Therefore, 47283 is divisible by 3 but not divisible by 2

Hence, 47283 is not divisible by 6

**Problem 5 – Divisibility rule for 6**

Check whether 64848 is divisible by 6?

**a) Yes**

b) No

Solution:

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

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, 64848

8 is at one’s place

and 8 is divisible by 2

So, 64848 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, 64848

Sum of its digits = 6 + 4 + 8 + 4 + 8 = 30

and 30 is divisible by 3

So, 64848 is also divisible by 3

Therefore, 64848 is divisible by 2 and 3

Hence, 64848 is also divisible by 6