## 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?

by BTGmoderatorDC » Tue Oct 26, 2021 7:43 pm

00:00

A

B

C

D

E

## Global Stats

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

by swerve » Wed Oct 27, 2021 7:59 am
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

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