Question

Find the smallest number by which the following number must be multiplied to obtain a perfect cube:

$256$

• A. $2$
• B. $1$
• C. $4$
• D. $8$

Answer 1

The correct option is A $2$

Prime factorizing $256$, we get,

$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^8$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.
Here, number of $2$'s is $8$.

So we need to multiply another $2$ in the factorization to make $256$ a perfect cube.

Hence, the smallest number by which $256$ must be multiplied to obtain a perfect cube is $2$.

Therefore, option $A$ is correct.