Question

last two digit of (245)^23
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Answer 1

Given:

Number given = 245²³

To Find:

Last two digits of 245²³.

Solution:

Number ending with 5 will always have either 75 or 25 as the last two digits.

So we have to find whether the second last digit is 7 or 5 .

Now we have to consider the second last digit of base of a number and the power.

Here the second last digit of the base is 4 which is even, and the power is 23 which is odd then the second last digit of the answer will be 2.

The table is like this:

second last digit of base         Power          last two digits of answer

          Odd                                     Odd                   75

          Odd                                     even                  25

          Even                                    Odd                   25

          Even                                    Even                  25

Hence the last two digits of 245²³ are 25.