When 231 is divided by 5 the remainder is -

Answer: Option B

$${\text{2}}^{31}÷5$$
$$\begin{array}{c}\text{power }\text{ remainder}\text{hfill}\\ \left[\begin{array}{c}{2}^1\to \frac{2}{5}\to 2\text{hfill}\\ 2^2\to \frac{4}{5}\to 4\text{hfill}\\ 2^3\to \frac{8}{5}\to 3\text{hfill}\\ 2^4\to \frac{16}{5}\to 1\text{hfill}\end{array}\right]\text{cycle 1}\text{hfill}\\ \left[2^5\to \frac{243}{5}\to 2\right]\text{cycle 2}\text{hfill}\end{array}$$

$$\begin{array}{rl}& \text{Divided = }\frac{2^{31}}{5}=\frac{2^{4\times 7}\times 2^3}{5}\\ & \Rightarrow \text{remainder = 3}\\ & \text{So }{\text{2}}^3\text{ has 3 remainder }\\ & {\text{2}}^{31}\text{ has 3 remainder}\end{array}$$