Question

What is the least number by which 6750 may be divided so that the quotient is a perfect cube?

A: 2

B: 3

C: 5

D: 6

$\left[1\right]$

Answer 1

Answer: Option A

Let us prime factorize $6750$:
On finding the prime factors of $6750$, we get:
$6750=2\times 5\times 5\times 5\times 3\times 3\times 3=2\times (5\times 5\times 5)\times (3\times 3\times 3)$

Clearly, $6750$ must be divided by $2$ so that the quotient is a perfect cube.