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if n and p are different positive prime number, which of the

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Manager
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if n and p are different positive prime number, which of the [#permalink] New post 09 Nov 2003, 13:10
if n and p are different positive prime number, which of the intergers, "n^4","p^3" and "np" have exactly 4 positive divisors.
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 [#permalink] New post 09 Nov 2003, 16:36
I vote for n^4.

Divisors of n^4: n┬│, n┬▓, n and 1.
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 [#permalink] New post 10 Nov 2003, 09:29
guess it should be all.

3^3 = 27 has only 4 factors(1,27,3,9).

so is 35(=5*7) = (5,7,35,1).
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 [#permalink] New post 10 Nov 2003, 23:17
wonder_gmat wrote:
I vote for n^4.

Divisors of n^4: n┬│, n┬▓, n and 1.


disagree. I forgot about n^4 itself.
I vote for np. Its divisors are: np, n, p, and 1—exactly four
Oddly enough, p^3 also has exactly four divisors: p^3, p^2, p, and 1.
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 [#permalink] New post 12 Nov 2003, 17:25
Interestingly I changed my original intuition about the number itself being it's own divisor. After seeing there are two choices that will make the answer list, I figured it just may be one of those odd problems that would say you couldn't use the number itself as it's own divisor. Eh, oh well! :-D
  [#permalink] 12 Nov 2003, 17:25
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