For any number * 2^n*(or

*), if you need to find out if it is a factor of number X, it is enough if you check the last n digits of the number X.*

**5^n**For ex., say a number 12**0016,** if I need to find if the number is divisible by 16(=2^4), I just need to check if the last 4 digits is divisible by 4. So here 12** 0016 **is divisible by 16, because the last 4 digit is divisible by 16.

Now, let’s not convinced just with some shortcut.

Let’s understand the concept by taking a 5 digit number represented by * abcde*, where a,b,c,d,e each represents some decimal from 0 to 9.

I need to find out if the number * abcde* is divisible by 8(=2^3).

Expressing the number * abcde* as

*ab000 +cde*So now, * ab000 *is nothing but

*, no doubt this is divisible by 8.*

**abX1000**Now we just need to confirm if the number * cde *is divisible by 8. That’s it for any number

*X*, to confirm if it is divisible by

*we just need to check if the last n digits is divisible by n.*

**2^n**The similar way we can prove for powers of 5..