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1. Find the remainder when 67¹⁰⁷ is divided by 7.

A. 4

B. 2

C. 1

D. 6

Solution:

\begin{aligned} \frac{67^{107}}{7} \\ O r, \frac{{(7 \times 9 + 4)}^{107}}{7} \\ The remainder will be same as \\ \frac{4^{107}}{7} \\ O r, \frac{4^{3}}{7} \\ O r, \frac{64}{7} \\ Required Remainder = 1 \end{aligned}

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