Finding Last Two digits
Concepts Examples

There can be direct questions on finding last two digits of any power of a natural number and this is very important for eliminating options in questions. Following are the four simple cases with which we will be able to solve almost every problem.

Rules for Finding Last Two Digits of square of a number

In order to find the last two digits of square of any two digit number number, we can write it as difference or sum from 50 or 100, whichever is closer. In general the last two digits of a number (50±k)2 or (100-k)2 will be determined by square of k.

e.g 472 can be written as (50-3)2,

Now, the last two digits will be determined by square of 3 that is 09

Rules for Finding Last Two Digits of any power of a number

1. For a natural number Nk, where N is a natural number ending with 0 and K is a natural number greater than 2,

Last two digits will always be 00.

2. For a natural number Nk, where N is a natural number ending with 5 and K is a natural number greater than 2,

Last two digits will always be 25.

3. For a natural number (2×m)40k+1, where m is a odd number not ending with 5 and K is a natural number,

Last two digits will always be (2×m +50).

4. For all the remaining cases, the last two digits of N40k+x,

Last two digits will always be equal to the last 2 digits of Nx