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

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by swerve » 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.
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by ceilidh.erickson » 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.

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by Scott@TargetTestPrep » Tue Oct 29, 2019 6:39 pm
swerve wrote: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.
The factors of n that are greater than or equal to 8 and less than or equal to 30 are:

3 x 5 = 15

2 x 5 = 10

2 x 3 x 5 = 30

2^2 x 3 = 12

2^2 x 5 = 20

2^3 = 8

2^3 x 3 = 24

and

2^4 = 16

So there are 8 such factors.

Answer: A

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