Question

The remainder obtained when ${96}^{96}$ is divided by 7 is

• A. 0
• B. 95
• C. 1
• D. 94

Answer 1

The correct option is C

1

$\frac{{96}^{96}}{7}$ remainder is same when $\frac{-2^{96}}{7}$

since the power is even
$\frac{-2^{96}}{7}$ remainder is same when $\frac{2^{96}}{7}$

$\frac{2^{[}{3}^{32}]}{7}$ remainder is same when $\frac{8^{32}}{7}$

$\frac{8^{32}}{7}$ remainder is same when $\frac{1^{32}}{7}$

So the remainder is 1 ( Remainder obtained in $\frac{ab}{c}$ is same as remainder obtained by multiplying the individual remainders obtained in $\left(\frac{a}{c}and\frac{b}{c}\right)$ when divided by c , where a,b and c are integers )