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

[BTGmoderatorDC]

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

[swerve]

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