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If 52/x is a positive integer, how many integer values are p

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If 52/x is a positive integer, how many integer values are p [#permalink] New post 18 Jul 2018, 16:49
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If \(\frac{52}{x}\) is a positive integer, how many integer values are possible for x?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 10
[Reveal] Spoiler: OA

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Re: If 52/x is a positive integer, how many integer values are p [#permalink] New post 18 Jul 2018, 20:00
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Carcass wrote:
If \(\frac{52}{x}\) is a positive integer, how many integer values are possible for x?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 10


Factors of 52 are = 52 , 26, 13 , 4 , 2 and 1

so there are \(6\) possible values for x
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Re: If 52/x is a positive integer, how many integer values are p [#permalink] New post 19 Jul 2018, 12:12
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Carcass wrote:
If \(\frac{52}{x}\) is a positive integer, how many integer values are possible for x?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 10



If we want to make x an integer x has to be the factors of 52.

So,

52 = 26*2 = 13 * \(2^2\)

there is a shortcut to find out the total factor. Just add 1 to the power of the prime.

so, (1+1)*( 2+1) = 6

The best answer is B.
Re: If 52/x is a positive integer, how many integer values are p   [#permalink] 19 Jul 2018, 12:12
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If 52/x is a positive integer, how many integer values are p

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