Question

Find the smallest number which should be multiplied to $1352$ to get a perfect cube.

• A. $12$
• B. $13$
• C. $61$
• D. $21$

Answer 1

The correct option is B $13$

By prime factorising $1352$,

we get, $1352=2\times 2\times 2\times 13\times 13$

$=2^3\times {13}^2$

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

Here, number of $2$'s is $3$ and number of $13$'s is $2$.

So we need to multiply another $13$ to the factorization to make $1352$ a perfect cube.

Hence, the smallest number by which $1352$ must be multiplied to obtain a perfect cube is $13$.