Question

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

• A. 4
• B. 8
• C. 2
• D. 6

Answer 1

Answer: (C)

Step 1:Finding a relation between exponents and last digit
$2^{1}=2$
$2^{2}=4$
$2^{3}=8$
$2^{4}=16$
$2^{5}=32$
The general trend is found to be that the last digit of
$2^{4 n+1}$ is $2$
$2^{4 n+2}$ is $4$
$2^{4 n+3}$ is $8$
$2^{4 n+4}$ is $6$
Step 2: Comparing
$2^{301}=2^{300+1}=2^{4 n+1}$
$\Rightarrow $ the last digit of $2^{301}$ is $2$
$\Rightarrow $ On dividing $2^{301}$ with $5$ gives you $2$ as the remainder