Question

Question 3(v)
Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:
704

Answer 1

704
Prime factors of $704=2\times 2\times 2\times 2\times 2\times 2\times 11$
Here one factor 11 does not appear in a triplet.
Therefore, 704 must be divided by 11 to make it a perfect cube.
$\begin{array}{cc}2& 704\\ 2& 352\\ 2& 176\\ 2& 88\\ 2& 44\\ 2& 22\\ 2& 11\\ & 1\end{array}$