### Brain Teasers

# Number of Divisors

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?

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?

### Hint

It looks like a math teaser, but look at its category.If your answer is 11, then you're tricked.

### Answer

Only one, because 1 is a good number!Hide Hint Show Hint Hide Answer Show Answer

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