Question

State whether the number given below is a perfect cube or not:
46656

Answer 1

Let us factorise 46656 using the prime factorisation method.

$\begin{array}{cc}2& 46656\\ 2& 23328\\ 2& 11664\\ 2& 5832\\ 2& 2916\\ 2& 1458\\ 3& 729\\ 3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

Prime factors of $46656=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3$
Here all factors appear in 3’sgroup.
Therefore, 46656 is a perfect cube.