Question

Find the smallest number by which $4232$ must be multiplied to make it a perfect cube.

• A. $2$
• B. $17$
• C. $19$
• D. $23$

Answer 1

The correct option is D $23$

Prime factorising of $4232$ is as below,

$4232=2\times 2\times 2\times 23\times 23$

$=2^3\times {23}^2$.

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

Here, number of $2$'s is $3$ and number of $23$'s is $2$.

So we need to multiply another $23$ to the factorization to make $4232$ a perfect cube.

Hence, the smallest number by which $4232$ must be multiplied to obtain a perfect cube is $23$.

Hence, option $D$ is correct.