Question

What is the last digit of $2^{100}$?

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is C

6

Consider, $2^1=2$, last digit is 2

$2^2=4$, last digit is 4

$2^3=8$, last digit is 8

$2^4=16$, last digit is 6

$2^5=32$, last digit is 2

$2^6=64$, last digit is 4

$2^7=128$, last digit is 8

$2^8=256$, last digit is 6

We know that in case of 2, if the remainder when exponent divided by 4 is 1, 2, 3 and 0 we have last digit as 2, 4, 8 and 6 respectively.

When the power 100 is divided by 4, we get 0 as remainder.

Hence, we get last digit in $2^{100}$ as 6.