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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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20 May 2017, 07:12
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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

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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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20 May 2017, 07:30
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: $$(2+1)(2+1)=9$$

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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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20 May 2017, 08:08
Top Contributor
1
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!

Cheers,
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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17 Jan 2018, 09:38
Are there any practice problems exactly like this one elsewhere on the forums?
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Joined: 02 Sep 2009
Posts: 49892
Re: How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source:  [#permalink]

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17 Jan 2018, 10:04
1
Re: How many factors of 3600 are odd? A) 3 B) 6 C) 9 D) 18 E) 45 Source: &nbs [#permalink] 17 Jan 2018, 10:04
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