Question

What is the smallest number by which 392 must be multiplied, so that the product is a perfect cube?

• A. 7
• B. 6
• C. 4
• D. 5

Answer 1

The correct option is A

7

Given number is 392.
Prime factorisation of 392 is:
$\begin{array}{cc}2& 392\\ 2& 196\\ 2& 98\\ 7& 49\\ & 7\end{array}$

Hence, $392=2\times 2\times 2\times 7\times 7$

A number will a perfect cube, if all prime factors form a triplet.

Here, the number 7 occurs only twice.

Clearly, 392 must be multiplied by 7 in order to make it a perfect cube.