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Question

Given that 588p is a perfect cube, write down the smallest positive integer value of p.

Answer

588 = 2 x 294
= 2 x 2 x 147
= 2 x 2 x 3 x 49
= 2 x 2 x 3 x 7 x 7
= 22 x 3 x 72

We need 1 more 2, 2 more 3s and 1 more 7 to make all the factors a cube number.

2 x 7 x 3 x 3 = 126


Check

588 x 126 = 74,088

23 x 33 x 73
= (2 x 3 x 7) x (2 x 3 x 7) x (2 x 3 x 7)
= 42 x 42 x 42
= 423
= 74,088

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