Question

The product $864\times n$ is a perfect cube. What is the smallest possible value of '$n$'?

• A. $2$
• B. $1$
• C. $4$
• D. $3$

Answer 1

Answer: (A)

$2$

Factorizing $864$, we get

$864=3^3\times 2^5=3^3\times 2^3\times 2^2$

To make $864\times n$ perfect cube, $n$ needs to be equal to $2$ to make it $3^3\times 2^3\times 2^3$.