Question

Find the smallest number which should be multiplied to $231525$ to make it a perfect cube.

• A. $5$
• B. $3$
• C. $7$
• D. $21$

Answer 1

The correct option is A $5$

Prime factorising $231525$, we get,

$231525=3\times 3\times 3\times 5\times 5\times 7\times 7\times 7$

$=3^3\times 5^2\times 7^3$.

We know that a perfect cube number has its factor with an exponent as multiples of $3.$

Here, exponent of $3$'s is $3$, exponent of $5$'s is $2$ and exponent of $7$'s is $3$.

So we need to multiply another $5$ to the factorization to make $2,31,525$ a perfect cube.

Hence, the smallest number by which $2,31,525$ must be multiplied to obtain a perfect cube is $5$.

Hence, option $A$ is correct.