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In N is a positive integer and 14N/60 is an integer, then N has how ma

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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, 10:25
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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

Two Great questions Similar to this one => in-n-is-a-positive-integer-and-14n-60-is-an-integer-what-is-the-small-224146.html
in-n-is-a-positive-integer-less-than-200-and-14n-60-is-an-100763.html

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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, 10:33
2
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

Two Great questions Similar to this one => in-n-is-a-positive-integer-and-14n-60-is-an-integer-what-is-the-small-224146.html
in-n-is-a-positive-integer-less-than-200-and-14n-60-is-an-100763.html

"14N/60 is an integer" tells nothing more than N is a multiple of 30.

So, N could have n number of different prime factors. Hence, we don't know how many such factors do we have.
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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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Top Contributor
2
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.

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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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04 Dec 2018, 20:20
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Re: In N is a positive integer and 14N/60 is an integer, then N has how ma   [#permalink] 04 Dec 2018, 20:20
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