# Divisibility Rule by 6

If the given number is divisible by 2 and 3 both then we can say that the number is divisible by 6.

Example : Is 54 divisible by 6?

Solution : First check whether the given number is divisible by 2 or not. Then only check for 3.

Number is divisible by 2 if its last digits are 0, 2, 4, 6 or 8.

Here last digit of a number 54 is 4 means divisible by 2.

Now check for 3 whether the given number is divisible by 3 or not.

Number is divisible by 3 if sum of all digits are multiple of 3 or divisible by 3.

Here sum of all digits of given number is 54 i.e. 5 + 4 = 9 Which is multiple of 3. Means 54 is divisible by 3 also.

Hence 54 is divisible by 6.

Example : Is 682 divisible by 6?

Solution : First check whether the given number is divisible by 2 or not. Then only check for 3.

Number is divisible by to if its last digits are 0, 2, 4, 6 or 8.

Here last digit of a number 682 is 2 means divisible by 2.

Now check for three whether the given number is divisible by 3 or not.

Number is divisible by 3 if sum of all digits are multiple of 3 or divisible by 3.

Here sum of all digits of given number is 682 i.e. 6 + 8 + 2 = 16 Which is not multiple of 3 or we can say 16 is not divisible by 3. Means 682 is not divisible by 3.

Hence 682 is not divisible by 6.

Example : Is 84561 divisible by 6?

Solution : First check whether the given number is divisible by 2 or not. Then only check for 3.

Number is divisible by to if its last digits are 0, 2, 4, 6 or 8.

Here last digit of a number 84561 is 1 means not divisible by 2.

There is no need to check further that 84561 is divisible by 3 or not. Because number is only divisible by 6 if its divisible by 2 and 3 both.

Here in this case number is not divisible by 2. Hence 84561 is not divisible by 6.

### Let's have practice for divisibility rule by 6.

297, 286, 2664, 6588, 8451, 86586, 95642

Solution :

297 - Last digit 7 means not divisible by 2. Hence not divisible by 6.

286 - Last digit is 6 which is divisible by 2. (2 + 8 + 6 = 16) 16 is not divisible by 3.

Hence not divisible by 6.

2664 - Last digit is 4 which is divisible by 2. (2 + 6 + 6 + 4 = 18 ) 18 is divisible by 3.

Hence divisible by 6.

6588 - Last digit is 8 which is divisible by 2. ( 6 + 5 + 8 + 8 = 27) 27 is divisible by 3.

Hence divisible by 6.

8451 - Last digit 1 means not divisible by 2. Hence not divisible by 6.

86586 - Last digit is 6 which is divisible by 2. ( 8 + 6 + 5 + 8 + 6 = 33) 33 is divisible by

3. Hence divisible by 6.

95642Last digit is 2 which is divisible by 2( 9 + 5 + 6 + 4 + 2 =26) 26 is not divisible by 3. Hence not divisible by 6.

I hope you get the point of Divisibility Rule by 6

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