Question

if 2power 23 is divided by 5 what is the remainder

Answer 1

2 to the power 1 = 2

2 to the power 2 = 4

2 to the power 3 = 8

2 to the power 4 = 16; last digit = 6

So, 2,4,8,6 is the cycle for the digit 2.

2 to the power 23 will have last digit as 8.

Therefore, the remainder will be 3 when divided by 5.

For example: 13,23,33,43,53.... be it any number ending with 3 will have a remainder 3 when divided by 5.

Also, $2^{23}$ = 8388608.

On dividing it by 5 we get quotient as 1677721 and remainder as 3.

Answer 2

As per the question 23^2/5

Hence,

23^2 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 8388608

= 8388608/5

The quotient will be 1677721 whereas reminder will be 3