Question

The least remainder when ${17}^{30}$ is divided by 5 is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

$17=\left(mod5\right)$
$(17{)}^5=(2{)}^5\left(mod5\right)=2\left(mod5\right)$
$\Rightarrow ({17}^5{)}^6=(2{)}^6\left(mod5\right)\Rightarrow (17{)}^{30}=4(mod5)$
Hence required remainder = 4