Question

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

$675$

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is A $5$

Prime factorising $675$, we get,

$675=5\times 5\times 3\times 3\times 3$$=3^3\times 5^2$.

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

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

So we need to multiply another $5$ in the factorization to make $675$ a perfect cube.

Hence, the smallest number by which $675$ must be multiplied to obtain a perfect cube is $5$.

Therefore, option $A$ is correct.