Question

The smallest number by which 392 may be divided such that the quotient is a perfect cube

Answer 1

$factors \: of \: given \: number(392) = 2 \times 2 \times \times 2 \times 7 \times 7 \\ \: hence \: we \: divided \: by \: 49 \: then. the \: quotient \: is \: perfect \: cube \: \\ \: your \: answer = 49$

Answer 2

Product of prime factors of 392

392 = 2 x 2 x 2 x 7 x 7

clearly, to make a perfect cube, it must be divided by (7 x 7), i.e