Question

The remainder when $2^{2016}$ is divided by $63$ is:

• A. \( 1 \)
• B. \( 8 \)
• C. \( 17 \)
• D. \( 32 \)
• E. \( 61 \)

Hint:

Whenever the divisor is of the form \( 2^n - 1 \), the remainder of \( 2^{kn} \) will always be 1. Here, \( 63 = 2^6 - 1 \), and 2016 is a multiple of 6, so the result is immediately 1.

Answer 1

The Correct Option is A