If p is a prime number
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- DHILLONRAVI1983
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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?
- DavidG@VeritasPrep
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In general, try to start threads with questions that have the standard GMAT format (5 answer choices.) Within a given thread/topic, you should feel free to post whatever questions you like.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?
- DavidG@VeritasPrep
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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.)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?
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.'
- DHILLONRAVI1983
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David, what if q is 0?DavidG@VeritasPrep wrote: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.)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?
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.'
- DavidG@VeritasPrep
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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.DHILLONRAVI1983 wrote:David, what if q is 0?DavidG@VeritasPrep wrote: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.)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?
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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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.