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Number of Divisors

Trick brain teasers appear difficult at first, but they have a trick that makes them really easy.

 

Puzzle ID:#48551
Fun:** (2.03)
Difficulty:*** (2.14)
Category:Trick
Submitted By:shenqiangAcn****!!

 

 

 



We call a positive integer a "good number", if the product of all its divisors equals its cube.

For example, 12 is a good number, because the divisors of 12 are 1, 2, 3, 4, 6, 12, and 1*2*3*4*6*12=1728=12^3.

If n is a good number, what is the minimum number of divisors that n^2 has?





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