Question

Remainder for 3 to the power of 100 ÷ 7

Answer 1

$\frac{3^{100}}{7} \\ \frac{(3^{3})^{33} \times 3}{7} \\ \frac{27^{33} \times 3}{7}$

$\dfrac{(28-1)^{33} \times 3}{7}$

$\frac{(-1)^{33} \times 3}{7}$

$\frac{-3}{7}$

We have the negative remainder that is -3,

to find the positive remainder we just add 7 to it.

-3+7 = +4

So the remainder is +4