Question

What is the remainder when $2^{96}$ is divided by 96?

• A. 16
• B. 32
• C. 64
• D. 80

Answer 1

The correct option is C 64

The common factor between $2^{96}$ and 96 is 32.
Divide both dividend and divisor by 32.
Now, we will get the resulting dividend and the divisor and we will find the remainder when $2^{91}$ is divided by 3.
When $2^{91}$ is divided by 3, we get the remainder as -1 or +2(3-1). Now since we cancelled the common factor from both dividend & divisor, the final remainder will be obtained after multiplying the remainder with the cancelled number, so final remainder will be $+2\times 32=64.$