SOLUTION: How many positive factors of 72 are perfect cubes?

SOLUTION: How many positive factors of 72 are perfect cubes?

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Question 203556: How many positive factors of 72 are perfect cubes?
Answer by promotion analysis(5) (Show Source): You can put this solution on YOUR website!
One way to do this would be to factorize 72 into its prime factors and then test each combination to see if it is a perfect cube.

However, there is a very simple method in this case. The first four cubes (1 cubed, 2 cubed, 3 cubed, 4 cubed) are 1, 8, 27, 64.
Of these, only 1 and 8 are factors of 72.
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