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Question
With what least number must 8640 be divided so that the quotient is a perfect cube?
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Solution
The prime factors of 8640 are
= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × 5
Clearly, 8640 must be divided by 5. So, that the quotient is a perfect cube.
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