Question

What is the minimum number we need to multiply with 392 to make it a perfect cube?

• A. 4
• B. 7
• C. 2
• D. 6

Answer 1

The correct option is B 7

$\begin{array}{cc}2& 392\\ 2& 196\\ 2& 98\\ 7& 49\\ & 7\end{array}$

Prime factorization of $392=2\times 2\times 2\times 7\times 7$

For a perfect cube, the factors should form triplets. Here, 2 is forming the triplet but 7 is not.
To make it a perfect cube, we need to multiply it with 7.

$392\times 7=2\times 2\times 2\times 7\times 7\times 7$