Question

What is the smallest number by which $8640$ must be divided so that the quotient is a perfect cube?

Answer 1

$8640=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 5$
$5$ occurs as a prime number only once.
Hence, $5$ is the smallest number by which $8640$ must be divided, so that the quotient is a perfect cube.