A number is divisible by 6 if it is divisible by 2 and 3. or A number is divisible by 6 if its right digit (ones digit) is even and sum of its digits (all digits) is divisible by 3.

Let us we will apply this interesting math rule on following examples.

Is 168 divisible by 6?

The last digit (ones digit) 8 is divisible by 2, so the number 168 is divisible by 2.
And the sum of digits 15 is divisible by 3 so the number 168 is divisible by 3.
Now the number 168 is divisible by 2 and 3, so it is also divisible by 6
(Do these all steps in your mind).

Is 323 divisible by 6?

The last digit (ones digit) is 3 which is not divisible by 2, so the number 323 is not divisible by 2.
Here no need to check divisible by 3 because it will be an extra effort.
Now the number 323 is not divisible by 2, so it is not divisible by 6.
(Do these all steps in your mind).

Is 70006 divisible by 6?

The last digit (ones digit) 6 is even which is divisible by 2 so the number 70006 is not divisible by 2.
And the sum of digits is 13 which is not divisible by 3 so the number 70006 is not divisible by 3.
Now the number 70006 is divisible by 2 but not divisible by 3, so it is not divisible by 6.
(Do these all steps in your mind).

Is 122220 divisible by 6?

Its right digit (ones digit) is 0 which is even and divisible by 2 so the number 122220 is divisible by 2.
And the sum of its all digit is 9 which is divisible by 3 so the number 122220 is divisble by 3.
Now the number 122220 is divisible by 2 and 3, so it is also divisible by 6.
(Do these all steps in your mind).

Is 10987 divisible by 6?

Its right digit (ones digit) is 7 which is not divisible by 2 so the number 10987 is not divisble by 2.
And the sum of its all digit is 25 which is also not divisible by 3.
Now the number 10987 is not divisible by 2 nor divisible by 3, so it is not divisible by 6.
(Do these all steps in your mind).