Question

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

• A. $2$
• B. $1$
• C. $4$
• D. $3$

Answer 1

Answer: (C)

$4$

$(17{)}^{30}=(15+2{)}^{30}$

All the terms in the expansion of the above expression except the last, would be divisible by $5$.

So, we indirectly need to find the remainder when $2^{30}$ is divided by $5.$

$2^{30}=(2^5{)}^6={32}^6$

Since $32$ leaves remainder $2$ when divided by $5,{32}^6$ would leave remainder $2^6$ when divided by $5$.

i.e. when $64$ is divided by $5$, which is when the remainder turns out to be $4$.

Hence the answer is option C.