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If p is a prime number

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by DavidG@VeritasPrep » Mon Oct 31, 2016 6:35 pm
DHILLONRAVI1983 wrote:If p is a prime number and q is a non prime integer, what are the minimum and maximum number of factors p and q can have in common?
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by DavidG@VeritasPrep » Mon Oct 31, 2016 6:37 pm
DHILLONRAVI1983 wrote:If p is a prime number and q is a non prime integer, what are the minimum and maximum number of factors p and q can have in common?
We know that a prime, by definition, only has two factors: 1 and itself. So the maximum # of factors in common would be two. (As an example, say p = 3 and q = 9. The two factors in common are 1 and 3.)

If we assume that q is a positive integer, then the two numbers will have to have '1' in common. For example, if p = 2 and q = 9, the two numbers would only share one factor, '1.'
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by DHILLONRAVI1983 » Tue Nov 01, 2016 10:32 am
DavidG@VeritasPrep wrote:
DHILLONRAVI1983 wrote:If p is a prime number and q is a non prime integer, what are the minimum and maximum number of factors p and q can have in common?
We know that a prime, by definition, only has two factors: 1 and itself. So the maximum # of factors in common would be two. (As an example, say p = 3 and q = 9. The two factors in common are 1 and 3.)

If we assume that q is a positive integer, then the two numbers will have to have '1' in common. For example, if p = 2 and q = 9, the two numbers would only share one factor, '1.'
David, what if q is 0?
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by DavidG@VeritasPrep » Tue Nov 01, 2016 10:50 am
DHILLONRAVI1983 wrote:
DavidG@VeritasPrep wrote:
DHILLONRAVI1983 wrote:If p is a prime number and q is a non prime integer, what are the minimum and maximum number of factors p and q can have in common?
We know that a prime, by definition, only has two factors: 1 and itself. So the maximum # of factors in common would be two. (As an example, say p = 3 and q = 9. The two factors in common are 1 and 3.)

If we assume that q is a positive integer, then the two numbers will have to have '1' in common. For example, if p = 2 and q = 9, the two numbers would only share one factor, '1.'
David, what if q is 0?
An excellent question. Technically, 0 has an infinite number of factors. So if p = 2 and q = 0, we know that '1' and '2' are both factors of two, and every positive integer would be a factor of 0, so they'd share two factors (1 and 2) in common, though this doesn't feel intuitive. Typically, when we're talking about common factors and multiples, the GMAT will invoke the restriction that we're dealing with positive numbers.
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by Matt@VeritasPrep » Fri Nov 11, 2016 4:27 pm
That positive restriction is a definite characteristic of the GMAT: "the maximum is infinity" does not sound like something that would appear on the GMAT in any form.
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