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# If integer n has exactly 3 positive factors, including 1 and

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If integer n has exactly 3 positive factors, including 1 and [#permalink]  30 Jun 2008, 12:37
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If integer n has exactly 3 positive factors, including 1 and n, how many positive divisors does n^2 have?

a. 4
b. 5
c. 6
d. 8
e. 9

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Joined: 28 Dec 2004
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Location: New York City
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Re: PS: Number properties [#permalink]  30 Jun 2008, 12:42
vksunder wrote:
If integer n has exactly 3 positive factors, including 1 and n, how many positive divisors does n^2 have?

a. 4
b. 5
c. 6
d. 8
e. 9

usually the square of a prime number has 3 factors..

so take 2^2=4 has 3 factors, so does 9 and 25 etc..

4^2=16...

factors are 1, 2, 4, 8, 16..

9^2=81 factors are 1, 3, 9, 27, 81
i.e 5 factors
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Re: PS: Number properties [#permalink]  30 Jun 2008, 12:46
vksunder wrote:
If integer n has exactly 3 positive factors, including 1 and n, how many positive divisors does n^2 have?

a. 4
b. 5
c. 6
d. 8
e. 9

Since this is a problem solving question (not DS), we can just pick a number that satisfies the initial constraints and apply it to the question.

4 and 9 are two examples where there are exactly 3 factors including and 1 and n.
4 = 1, 2, 4
9 = 1, 3, 9

For 4^2 = 16 and the factors of 16 are 1, 2, 4, 8, and 16 -->total of 5
For 9^2 = 81 and the factors of 81 are 1, 3, 9, 27, and 81 -->total of 5

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Factorials were someone's attempt to make math look exciting!!!

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Re: PS: Number properties [#permalink]  30 Jun 2008, 12:52
n has exactly 3 positive factors -> n = p^2 -> n^2 = p^4 -> 5 factors -> B
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
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Re: PS: Number properties [#permalink]  30 Jun 2008, 12:59
maratikus wrote:
n has exactly 3 positive factors -> n = p^2 -> n^2 = p^4 -> 5 factors -> B

yeah..nice method just remember that P^N...where N+1= equal to number of factors..
Re: PS: Number properties   [#permalink] 30 Jun 2008, 12:59
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