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# If p and q are prime numbers, how many divisors does the

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Intern
Joined: 05 Dec 2008
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If p and q are prime numbers, how many divisors does the [#permalink]  06 Dec 2008, 18:29
If p and q are prime numbers, how many divisors does the product (p^5)(q^8) have?

(A) 13
(B) 25
(C) 40
(D) 48
(E) 54
Manager
Joined: 23 Nov 2008
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Re: Counting challenge question #2 (harder) [#permalink]  06 Dec 2008, 18:54
Should be 6*9 = 54

p^5q^8 will give us 5*8 combinations, also need to add those with only p or q
easier to simply include p^0 and q^0, and use 6 and 9
Intern
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Re: Counting challenge question #2 (harder) [#permalink]  07 Dec 2008, 19:54
Yes, exactly 54
the form of factors of (p^5)(q^8) is (p^m)(q^n),in which:
0<=m<=5(6 values); 0<=n<=8 (9 valuess)
So there are 6*9=54 factors.
Re: Counting challenge question #2 (harder)   [#permalink] 07 Dec 2008, 19:54
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