Question

The remainder when ${27}^{40}$ is divided by $12$ is

• A. $3$
• B. $7$
• C. $9$
• D. $11$

Answer 1

The correct option is A $3$

${27}^{40}=3^{120}$ is divided by $12$,

$\frac{3^{120}}{12}=\frac{3^{119}}{4}$

When the power is odd, the remainder turns out to be $3$, and when the power is even, the remainder turns out to be $1$.

Power of $3$ is $119$ which is odd

Hence, the answer is $3$.