Find the smallest number by which 704 must be divided to obtain a perfect cube.

$704=\underline{2\times 2\times 2}\times \underline{2\times 2\times 2}\times 11$

Here, 11 is left after grouping in triplets. So, 704 is not a perfect cube. 

In the factorisation 11 appears only one time. If we divide the number by 11, then it will become a perfect cube.

So, $704÷11=\underline{2\times 2\times 2}\times \underline{2\times 2\times 2}=64$ is a perfect cube.
Hence, the smallest natural number by which 704 should be divided to make it a perfect cube is 11.