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

Question

How many even factors does 4500 have? A) 36 B) 24 C) 18 D) 12 E) 10 Source: www.GMATinsight.com

GMATinsight · Accepted Answer

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

Answer: Option B

eliaslatour · Answer

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
Answer choice (B).

PKN · Answer

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)

bumpbot · Answer

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

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

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