For any number
5^n), 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.
For ex., say a number
120016, if I need to find if the number is divisible by
2^4), I just need to check if the last 4 digits is divisible by
4. So here
120016 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
I need to find out if the number
abcde is divisible by
Expressing the number abcde as
ab000 is nothing but
abX1000, no doubt this is divisible by 8. Because
1000 is a factor for it which is multiple of
Now we just need to confirm if the number
cde is divisible by 8. The same applies for any number X , to confirm if it is divisible by
2^n we just need to check if the last n digits is divisible by n.
The similar way we can prove for powers of
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