Question

Find the smallest number which should be multiplied to $10976$ to get a perfect cube.

Answer 1

Prime factorising $10976$, we get,

$10976=2\times 2\times 2\times 2\times 2\times 7\times 7\times 7$

$=2^5\times 7^3$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.

Here, number of $2$'s is $5$ and number of $7$'s is $3$.

So we need to multiply another $2$ to the factorization to make $10976$ a perfect cube.

Hence, the smallest number by which $10976$ must be multiplied to obtain a perfect cube is $2$.