Question

The smallest number by which $2560$ must be multiplied so that the product is a perfect cube is?

• A. $5$
• B. $25$
• C. $10$
• D. $15$

Answer 1

The correct option is B $25$

Prime factorising $2560$, we get,

$2560=2^9\times 5$.

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

Here, number of $2$'s is $9$ and number of $5$'s is $1$.

So we need to multiply another $5^2$ in the factorization to make $2560$ a perfect cube.

Hence, the smallest number by which $2560$ must be multiplied to obtain a perfect cube is $5^2=25$.

Therefore, option $B$ is correct.