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Re: In N is a positive integer and 14N/60 is an integer, then N has how ma [#permalink]

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23 Aug 2016, 10:50

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stonecold wrote:

If N is a positive integer and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2 B. 3 C. 5 D. 6 E. cannot be determined

14N/60 = (2)(7)(N)/(2)(2)(3)(5) = (7)(N)/(2)(3)(5) For (7)(N)/(2)(3)(5) to be an integer, N must have a 2, 3 and 5 in its prime factorization (so the 2, 3 and 5 can cancel out in the denominator). So, for example, if N = (2)(3)(5), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)/(2)(3)(5) = 7, which is an integer.

Likewise, if N = (2)(3)(5)(7), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)/(2)(3)(5) = (7)(7) = 49, which is an integer. Also, if N = (2)(3)(5)(7)(11), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)(11)/(2)(3)(5) = (7)(7)(11), which will evaluate to be an integer. If N = (2)(3)(5)(7)(11)(13), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)(7)(11)(13)/(2)(3)(5) = (7)(7)(11)(13), which will evaluate to be an integer. And so on....

As we can see, we can continue this line of reasoning so that N has EVERY PRIME number in its prime factorization. Answer:

Re: In N is a positive integer and 14N/60 is an integer, then N has how ma [#permalink]

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22 Sep 2017, 09:07

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