Question

Given that 6048 = 2^5 • 3^3 • 7,

find the smallest possible integer value of n for 6048y to be a perfect cube number, giving your answer as the product of its prime factors.
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Answer 1

6048 should be multiplied by 98.

Explanation:

6048 = 2⁵ * 3³ * 7

To make 6048 a perfect cube, 6048 should be multiplied by 2 * 7 * 7.

2* 7 *7 = 98

Check: 6048 * 98 = 592704

592704 = 2⁶ * 3³ * 7³

`\sqrt[3]{592704}= 2 * 2 * 3 * 7`

= 84