Question

The remainder when $2^{100}$ is divided by $7$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$2$

$\frac{2^{100}}{7}=\frac{(2^{10}{)}^{10}}{7}$

remainder will be same for $\frac{2^{10}}{7}$ and $\frac{2^{100}}{7}$

So calculate remainder for,

$\frac{2^{10}}{7}=\frac{1024}{7}=2$

As the remainder of $\frac{2^{10}}{7}$ is $2$ then the remainder of $\frac{2^{100}}{7}$ is also $2$