Question

By what number $4320$ must be multiplied to obtain a number which is a perfect cube?

• A. $60$
• B. $45$
• C. $50$
• D. $55$

Answer 1

Answer: (C)

$50$

Prime factorising $4320$, we get,

$4320=2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 5$

$=2^5\times 3^3\times 5^1$.

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

Here, number of $2$'s is $5$, number of $3$'s is $3$ and number of $5$'s is $1$.

So we need to multiply another $2$, and $5^2$ in the factorization to make $4320$ a perfect cube.

Hence, the smallest number by which $4320$ must be multiplied to obtain a perfect cube is $2\times 5^2=50$.

Hence, option $C$ is correct.