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# If p and q are positive integers, is every factor of p a fac

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Manager
Joined: 10 Mar 2013
Posts: 112
If p and q are positive integers, is every factor of p a fac  [#permalink]

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21 Apr 2013, 06:07
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Difficulty:

55% (hard)

Question Stats:

51% (01:04) correct 49% (01:19) wrong based on 118 sessions

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If p and q are positive integers, is every factor of p a factor of q?

(1) p is a factor of q.

(2) The product of the prime factors of p is a factor of q.
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Joined: 02 Sep 2009
Posts: 54434
Re: If p and q are positive integers, is every factor of p a fac  [#permalink]

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21 Apr 2013, 07:15
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If p and q are positive integers, is every factor of p a factor of q?

(1) p is a factor of q. Since p is a factor of q (q/p=integer), then obviously every factor of p will be a factor of q. Sufficient.

(2) The product of the prime factors of p is a factor of q. If p=36 and q=6, then the product of the prime factors of p (2*3=6) IS a factor of q but not every factor of p is a factor of q (for example 36 is not a factor of 6). Though if p=q=6, then we'll have that every factor of p a factor of q. Not sufficient.

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Re: If p and q are positive integers, is every factor of p a fac  [#permalink]

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02 Sep 2017, 08:00
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Re: If p and q are positive integers, is every factor of p a fac   [#permalink] 02 Sep 2017, 08:00
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