For any number **2^n**(or **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 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 **abX1000**, no doubt this is divisible by 8.

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 **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 5..

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## Author: kannan_r

Just one among million. Software Engineer by profession. A bit interested in Math and Computing. Sometimes feeling that my interests are worth to be recorded and shared. This is just an initiative for my sharing;-)
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