Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 May 2013, 13:43

# number of divisors for prime numbers

Author Message
TAGS:
Manager
Joined: 03 Feb 2010
Posts: 68
Followers: 1

Kudos [?]: 2 [0], given: 4

number of divisors for prime numbers [#permalink]  01 Jul 2010, 16:48
00:00

Question Stats:

78% (01:34) correct 21% (00:33) wrong based on 2 sessions
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 ???
[Reveal] Spoiler: OA
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11633
Followers: 1802

Kudos [?]: 9611 [0], given: 829

Re: number of divisors for prime numbers [#permalink]  01 Jul 2010, 17:06
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 above p^3*q^6 will have (3+1)(6+1)=28 different positive factors.

Hope it helps.
_________________
Re: number of divisors for prime numbers   [#permalink] 01 Jul 2010, 17:06
Similar topics Replies Last post
Similar
Topics:
Prime number 5 03 Jan 2007, 23:32
prime numbers 5 05 Oct 2008, 12:15
If p and q are prime numbers, how many divisors does the 2 06 Dec 2008, 19:29
2 Number Properties, Divisors 5 06 Oct 2009, 03:46
5 Divisors of Prime numbers 19 11 Jan 2010, 12:26
Display posts from previous: Sort by