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

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If p and q are prime numbers, how many divisors does the pro [#permalink] New post 01 Jul 2010, 15:48
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If p and q are prime numbers, how many divisors does the product p^3*q^6 have?

(A) 9
(B) 12
(C) 18
(D) 28
(E) 363
[Reveal] Spoiler: OA
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Re: number of divisors for prime numbers [#permalink] New post 01 Jul 2010, 16:06
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ksharma12 wrote:
If p and q are prime numbers, how many divisors p^3*q^6 does the product have?


(A) 9 (B) 12(C) 18(D) 28(E) 363 ???


Finding the Number of Factors of an Integer:

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.


Back to the original question:

According to the above, p^3*q^6 will have (3+1)(6+1)=28 different positive factors.

Answer: D.

Hope it helps.
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Re: number of divisors for prime numbers [#permalink] New post 22 Sep 2013, 19:17
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Re: number of divisors for prime numbers   [#permalink] 22 Sep 2013, 19:17
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