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# How many even factors does 4500 have? A) 36 B) 24 C) 18 D)

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SVP
Joined: 08 Jul 2010
Posts: 2115
Location: India
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How many even factors does 4500 have? A) 36 B) 24 C) 18 D) [#permalink]

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26 May 2017, 05:05
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:10) correct 44% (01:07) wrong based on 95 sessions

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How many even factors does 4500 have?

A) 36
B) 24
C) 18
D) 12
E) 10

Source: www.GMATinsight.com

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SVP
Joined: 08 Jul 2010
Posts: 2115
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: How many even factors does 4500 have? A) 36 B) 24 C) 18 D) [#permalink]

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26 May 2017, 05:26
3
GMATinsight wrote:
How many even factors does 4500 have?

A) 36
B) 24
C) 18
D) 12
E) 10

Source: http://www.GMATinsight.com

Method 1: Total Number of factors - All odd factors

Prime factorised form
4500 = 2^2*3^2*5^3
Total Factors of 4500 = (2+1)*(2+1)*(3+1) = 3*3*4 = 36
Odd factors of 4500 = Factors without considering 2 as part of number = (2+1)*(3+1) = 3*4 = 12
Total Even Factors = 36-12 = 24

Method 2: Direct calculation of even Factors with minimum power of 2 being 1
Total Factors of 4500 = (2+1)*(2+1)*(3+1) = 3*3*4 = 36
Even factors of 4500 = Factors considering minimum power of 2 as 1= (1+1)*(2+1)*(3+1) = 2*3*4 = 24

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Re: How many even factors does 4500 have? A) 36 B) 24 C) 18 D) [#permalink]

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26 May 2017, 05:55
GMATinsight wrote:
How many even factors does 4500 have?

A) 36
B) 24
C) 18
D) 12
E) 10

Source: http://www.GMATinsight.com

Well, 4500 is 45x10x10 or 5x9 x 2x5 x 2x5

So I come up with prime factors of 2*2*3*3*5*5*5

Since it must be even, I'm going to include the first two to force an even result.

Then I can include the other 2 or not (2 choices).
I can include 0-2 3s (3 choices).
And I can include 0-3 5s (4 choices).

2 choices * 3 choices *4 choices = 24 choices
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Re: How many even factors does 4500 have? A) 36 B) 24 C) 18 D) [#permalink]

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03 Jun 2018, 23:33
GMATinsight wrote:
How many even factors does 4500 have?

A) 36
B) 24
C) 18
D) 12
E) 10

Source: http://www.GMATinsight.com

Prime factorization of 4500=$$2^2$$*$$3^2$$*$$5^3$$

Total no of factors of 4500= (2+1)(2+1)(3+1)=36

Total no of even factors=Total no of factors-Total no of odd factors

Since $$2^2$$ yields even factors, hence excluding it; we have $$3^2$$*$$5^3$$ which has (2+1)(3+1)=12 odd factors.

Hence, Total no of even factors of 4500=36-12=24

Therefore, correct answer option is (B)
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Re: How many even factors does 4500 have? A) 36 B) 24 C) 18 D)   [#permalink] 03 Jun 2018, 23:33
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