Question

When $2^{301}$ is divided by $5$, the least positive remainder is

• A. $4$
• B. $8$
• C. $2$
• D. $6$

Answer 1

The correct option is C $2$

Since, $2^1=2,2^2=4,2^3=8,2^4=16,2^5=32$. It is clear that unit place is repeated after every four power.

Then, $2^{301}=(2^4{)}^{75}\cdot 2$

$=(16{)}^{75}\cdot 2$

$\therefore$ Digit at unit place in $(16{)}^{75}$ is $6$.

$\therefore$ Digits at units place in $2^{301}$

$=$ digit at units place in $\left(6\right)\times 2$

$=2$

Hence, the remainder, when $2^{301}$ is divided by $5$, is $2$.