Question

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

• A. 1
• B. 8
• C. 17
• D. 32

Answer 1

Answer: (A)

1

Answer 2

$2^{2016}=\left(2^{6}\right)^{336}=(64)^{336}=(63+1)^{336}$

$(63+1)^{336}=^{366}C_0(63)^0(1)^{366}+^{366}C_1(63)^1(1)^{364}+^{366}C_2(63)^2(1)^{362}+…… = 1+63K$

$\therefore$ Remainder $=1$

So, the correct option is (A): $1$