Question

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

• A. $1$
• B. $8$
• C. $17$
• D. $32$
• E. $61$

Answer 1

The correct option is A $1$

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

${}^{366}{C}_0\left(63{)}^0\right(1{)}^{366}+{}^{366}{C}_1\left(63{)}^1\right(1{)}^{364}+{}^{366}{C}_2\left(63{)}^2\right(1{)}^{362}\dots \cdots =1+63\lambda$

$\therefore$ Remainder is $=1$ when $2^{2016}$ is divided by $63.$