# N has precisely 10 positive divisors. N has precisely 15 positive divisors. N has precisely 20 positive divisors....

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N has precisely 10 positive divisors.
N has precisely 15 positive divisors.
N has precisely 20 positive divisors.
N has precisely __ positive divisors.

posted Jun 13, 2017
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We are given a positive integer N. Two of its positive divisors are chosen and the differences between N and these two divisors are 270 and 280 respectively.

Find the number of possible value(s) of N?

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?

``````Number    Number of positive divisors