Ashish, we have three responses for you.

Ashish,

I'll show you for n = 2 and you can do the general situation.

Suppose that your integer is k then you can write

k = p * 100 + q * 10 + r

where p is an integer and q and r are digits. For example 25654 = 25600 + 50 + 4 = 25600 + 54.

Since p * 100 is divisible by 2² = 4, k is divisible by 2² if and only if q * 10 + r is divisible by 2² .

I hope this helps,
Penny

In our March Problem of the Month this year, you find the following argument:

A number N  can be written K x (2ⁿ x 5ⁿ ) + (the number formed by the last n digits).

Claude.

Another example: What you need to think about is the part of the number appearing before the last n digits. Look at 35640 for example.  This means 35 x 1000 + 640 = 35 x 10³ + 640.  What do you know about 2³ dividing 10³ ?

Penny