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How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source:

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How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source: [#permalink]

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New post 20 May 2017, 06:12
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How many factors of 3600 are odd?

A) 3
B) 6
C) 9
D) 18
E) 45

Source: www.GMATisnight.com
[Reveal] Spoiler: OA

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Re: How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source: [#permalink]

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New post 20 May 2017, 06:30
GMATinsight wrote:
How many factors of 3600 are odd?

A) 3
B) 6
C) 9
D) 18
E) 45

Source: http://www.GMATisnight.com


First, prime factorization: \(3600 = 36 \times 100 = (2^2 \times 3^2) \times (2^2 \times 5^2)=2^4 \times 3^2 \times 5^2\)

To count the number of odd factors, first we need to remove even prime: \(3^2 \times 5^2\).

Now, the number of odd factors is: \((2+1)(2+1)=9\)

The answer is C.
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Re: How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source: [#permalink]

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New post 20 May 2017, 07:08
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GMATinsight wrote:
How many factors of 3600 are odd?

A) 3
B) 6
C) 9
D) 18
E) 45

Source: http://www.GMATisnight.com


Since most of the answer choices are pretty small, it might not take long to LIST all of the odd factors.
We'll use the fact that 3600 = (2)(2)(2)(2)(3)(3)(5)(5) AND the fact that ODD x ODD = ODD
So, we'll work solely with the ODD primes: (3)(3)(5)(5)

So, the ODD factors of 3600 are:
- 1
- 3
- 5
- (3)(3) [we need not evaluate this, since we'll just going to count the factors in our list]
- (3)(5)
- (5)(5)
- (3)(3)(5)
- (3)(5)(5)
- (3)(3)(5)(5)

Done!

Answer:
[Reveal] Spoiler:
C


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Brent
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Re: How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source: [#permalink]

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New post 17 Jan 2018, 08:38
Are there any practice problems exactly like this one elsewhere on the forums?
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Re: How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source: [#permalink]

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New post 17 Jan 2018, 09:04
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destinyawaits wrote:
Are there any practice problems exactly like this one elsewhere on the forums?


Similar questions:
https://gmatclub.com/forum/how-many-odd ... 06082.html
https://gmatclub.com/forum/how-many-odd ... 93706.html
https://gmatclub.com/forum/the-number-o ... 65193.html
http://gmatclub.com/forum/how-many-of-t ... 00708.html
http://gmatclub.com/forum/how-many-even ... 32835.html
https://gmatclub.com/forum/how-many-dif ... 31425.html
https://gmatclub.com/forum/how-many-fac ... 41213.html
https://gmatclub.com/forum/how-many-eve ... 41209.html
https://gmatclub.com/forum/how-many-odd ... 33897.html
https://gmatclub.com/forum/how-many-fac ... 51831.html
https://gmatclub.com/forum/how-many-fac ... 51825.html

Hope it helps.
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Re: How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source:   [#permalink] 17 Jan 2018, 09:04
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