If 52/x is a positive integer, how many integer values are possible for x?

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If 52/x is a positive integer, how many integer values are possible for x?

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


OA B

Source: Manhattan Prep

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BTGmoderatorDC wrote:
Tue Oct 26, 2021 7:43 pm
If 52/x is a positive integer, how many integer values are possible for x?

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


OA B

Source: Manhattan Prep
\(\dfrac{52}{x} =\) positive integer. This means that \(x\) is a positive integer factor of \(52.\)

\(52\) is a composite number and can be expressed as \(52 = 2^2 \ast 13.\)

Number of positive integer factors of \(52 = (2+1) (1+1) = 3 \ast 2 = 6.\)

Therefore, the correct answer is B