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## If n=2^4*3*5, how many factors of n are...

tagged by: swerve

This topic has 1 expert reply and 0 member replies

### Top Member

swerve Master | Next Rank: 500 Posts
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#### If n=2^4*3*5, how many factors of n are...

Wed Nov 08, 2017 7:22 am
If n=2^4*3*5, how many factors of n are greater than or equal to 8 and less than equal to 30?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 15

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
Joined
04 Dec 2012
Posted:
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Wed Nov 08, 2017 11:43 am
There may be more formulaic strategies that you could use, but in this case (since it's a small-ish range), I'd just list out all the factors, then count:

n=2^4*3*5

Factors:
1
2
3
4
5
6
8
10
12
15
16
20
24
30

There are 8 distinct factors in this range. The answer is A.

Please list the source of your question!

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Ceilidh Erickson
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EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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