Question

Find the smallest number when it is multiplied by 392 , then the product is perfect cube.

(A) 3

(B) 5

(C) 6

(D) 7

Answer 1

$\begin{aligned}\begin{array}{r|l}2 & 392 \\\hline 2 & 196 \\\hline 2 & 98 \\\hline 7 & 49 \\\hline & 7 \\\therefore \quad 392= & 2 \times 2 \times 2 \times 7 \times 7 \\= & (2)^{3} \times 7 \times 7\end{array}\end{aligned}$

$\therefore$ The required no. $=7$; Ans.

Therefore, The correct option is (D)