Question

(i) Check the number 9648 is divisible by 6 or not.
(ii) Check the following number 9642 is divisible by both 6 and 8 or not?

Answer 1

If a number is divisible by both 2 and 3, then it will be divisible by 6 also.
Divisibility by 2
Here 9648 is divisible by 2 as the end with one of these (0, 2, 4, 6, 8) numbers or simply it is an even number.

Divisibility by 3
$\Rightarrow 9+6+4+8=27$
Here 27 is divisible by 3 hence 9648 is divisible by 3.
So, the number 9648 is divisible by both 2 and 3 and hence divisible by 6.

(ii) If a number is divisible by both 2 and 3, then it will be divisible by 6 also.
Divisibility by 2
Here 9642 is divisible by 2 as the end with one of these (0, 2, 4, 6, 8) numbers or simply it is an even number.

Divisibility by 3
$\Rightarrow 9+6+4+2=21$
Here 21 is divisible by 3 hence 9648 is divisible by 3.
So, the number 9642 is divisible by both 2 and 3 and hence divisible by 6.

Divisibility by 8 A number will be divisible by 8 only if the last three digits are divisible by 8.
The last 3 digits of 9642, i.e. 642 is not divisible by 8.
9642 is divisible by 6 but not by 8.