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.

95642 - Last 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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