Find the smallest number by which 81 must be divided to obtain a perfect cube.

$81=\underline{3\times 3\times 3}\times 3$

Here, 3 is left after grouping in a triplet. So, 81 is not a perfect cube. 

In the factorisation 3 appears only one time. If we divide the number by 3, then it will become a perfect cube.

So, $81÷3=\underline{3\times 3\times 3}=27$ is a perfect cube.
Hence, the smallest natural number by which 81 should be divided to make it a perfect cube is 3.