Find the remainder when 67107 is divided by 7.

Answer: Option C

$$\begin{array}{rl}& \frac{{67}^{107}}{7}\\ & Or,\frac{{\left(7\times 9+4\right)}^{107}}{7}\\ & \text{The}\text{remainder}\text{will}\text{be}\text{same}\text{as}\\ & \frac{4^{107}}{7}\\ & Or,\frac{4^3}{7}\\ & Or,\frac{64}{7}\\ & \text{Required}\text{Remainder}=1\end{array}$$