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

With what least number must 8640 be divided so that the quotient is a perfect cube?

The prime factors of 8640 are

= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5= (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) x 5

Clearly, 8640 must be divided by 5.

Concept: Cube Root Through Prime Factorisation Method

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