Question

What number must be multiplied to $6912$, so that the product becomes a perfect cube?

• A. $2$
• B. $3$
• C. $4$
• D. $6$
• E. $10$

Answer 1

The correct option is A $2$

Prime factorising $6912$, we get,

$6912=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$

$=2^8\times 3^3$.

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

Here, number of $2$'s is $8$ and number of $3$'s is $3$.

So we need to multiply another $2$ to the factorization to make $6912$ a perfect cube.

Hence, the smallest number by which $6912$ must be multiplied to obtain a perfect cube is $2$.

Hence, option $A$ is correct.