Find how many two-digit numbers are divisible by 6.

Given: Two-digit number from 10 to 99.

What to do: To find the two-digit number divisible by 6.

Solution: A two-digit number can be divisible by 6, then it must be divisible by 2 and 3 both.

Condition 1.

It should be an even number then it could be divisible by 2.

Condition 2.

Sum of its digits should be divisible by 3. And the number itself should be divisible by 3.

Now start with 10.

10 is an even number so it is divisible by 2 but it is not divisible by 3.

So it is not divisible by 6 also.

11 is not an even number and non-divisible by both 2 and 3.

But 12 is an even number and it is divisible by both 2 and 3. Then it is divisible by 6 also.

Similarly13, 14, 15, 16 and 17 aren’t divisible by 6 

But 18 fulfil the condition, divisible by both 2 and 3

$\therefore $two-digit numbers divisible by 6 between 10 to 99 are

12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90 and 96