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How many factors of 4500 are not divisible by 3? A) 36 B) 24 C) 18 D)

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GMATinsight
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How many factors of 4500 are not divisible by 3? A) 36 B) 24 C) 18 D) [#permalink] New post   Updated on: 26 May 2017, 05:42
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How many factors of 4500 are not divisible by 3?

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

Source: https://www.GMATinsight.com
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D

Originally posted by GMATinsight on 26 May 2017, 05:37.
Last edited by GMATinsight on 26 May 2017, 05:42, edited 1 time in total.
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Re: How many factors of 4500 are not divisible by 3? A) 36 B) 24 C) 18 D) [#permalink] New post   26 May 2017, 05:41
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GMATinsight wrote:
How many factors of 4500 are not divisible by 3?

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

Source: https://www.GMATinsight.com


Method :

Prime factorised form
4500 = 2^2*3^2*5^3
Factors of 4500 that are NOT multiples of 3 = Factors without considering 3 as part of number = (2+1)*(3+1) = 3*4 = 12

Answer: Option D
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Re: How many factors of 4500 are not divisible by 3? A) 36 B) 24 C) 18 D) [#permalink] New post   26 May 2017, 06:13
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GMATinsight wrote:
How many factors of 4500 are not divisible by 3?

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

Source: https://www.GMATinsight.com

Let me see... 4500 is 45 * 10 * 10 or (3*3*5) * (2*5) * (2*5)

So prime factors are 2*2 * 3*3 * 5*5*5

Since we don't want the number to be divisible by 3, we will exclude the 3s as choices.

0-2 2s = 3 choices
0-3 5s = 4 choices

So the answer should be around 12. But I wonder whether it is possible to include 0 2s and 0 5s and still come up with a factor. Let me think about that. I think the factor will be 1. That's a factor that includes no 2s and no 5s. So that's valid. I don't need to adjust the answer. I'll go with 12, which is answer choice (D).
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Re: How many factors of 4500 are not divisible by 3? A) 36 B) 24 C) 18 D) [#permalink] New post   26 May 2017, 07:58
Prime factorization: 4500=2^2*3^2*5^3. The number of factors not divisible by 3 is: 3*4=12.
Answer (D).

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Re: How many factors of 4500 are not divisible by 3? A) 36 B) 24 C) 18 D) [#permalink] New post   31 May 2018, 22:42
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Re: How many factors of 4500 are not divisible by 3? A) 36 B) 24 C) 18 D) [#permalink]
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