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How many factors of 3600 are even?
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19 Oct 2018, 06:11
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55% (01:27) correct 45% (01:10) wrong based on 116 sessions
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How many factors of 3600 are even? A) 9 B) 12 C) 24 D) 36 E) 45 Source: http://www.GMATinsight.com
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Re: How many factors of 3600 are even?
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19 Oct 2018, 08:18
GMATinsight wrote: How many factors of 3600 are even? A) 9 B) 12 C) 24 D) 36 E) 45 Source: http://www.GMATinsight.com\(3600=2^4*3^2*5^2\)... Best way is to find ODD factors and then subtract from total.. Total = \((4+1)(2+1)(2+1)=5*3*3=45\) Odd factors = \((2+1)(2+1)=3*3=9\) So rest are even factors = 459=36 D Various forms of this question are available
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Re: How many factors of 3600 are even?
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19 Oct 2018, 06:45
GMATinsight wrote: How many factors of 3600 are even? A) 9 B) 12 C) 24 D) 36 E) 45 Source: http://www.GMATinsight.com3600 = 100 * 36 = 4 * 25 * 6 * 6 = 2^2 * 5^2 * 2^2 * 3^2 = 2^4 * 3^2 * 5^2 Find the total factors  odd factors = even factors To find factors of a number we find the prime numbers = a^p * b^q... The number of factors will be = (p+1) * (q+1)... To find the number of odd factors we take all the other prime factors other than 2 in a similar fashion to the above We take the powers of odd primes = (2+1)*(2+1) = 9 Total = (4 + 1) (2+1) (2+1) = 5 * 3 * 3 = 45 45  9 = 36 Answer choice D I hope this helps! Posted from my mobile device



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Re: How many factors of 3600 are even?
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19 Oct 2018, 07:13
GMATinsight wrote: How many factors of 3600 are even? A) 9 B) 12 C) 24 D) 36 E) 45 Source: http://www.GMATinsight.comPrime factorise the number 3600 i.e. \(3600 = 2^4*3^2*5^2\) Row 1: 2^0, \(2^1, 2^2, 2^3, 2^4\) are factors of the number (except \(2^0\) because for number to be even every factor must have a minimum 21) Row 2: \(3^0, 3^1, 3^2\) are factors of the number Row 3: \(5^0, 5^1, 5^2\) are factors of the number Total number of factors = (4)*(3)*(3) = 36 Factors Answer: Option D
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How many factors of 3600 are even?
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Updated on: 04 Nov 2018, 05:36
First make prime factorization of 3600=2^4 * 3^2 * 5^2 where 2, 3, and 5 are prime factors of 4, 2 and 2 are their powers. The number of factors of 3600 will be expressed by the formula (p+1)(q+1)(r+1) where p,q and r are the powers.
According to the above the number of factors is (4+1)(2+1)(2+1)=45 factors...............................(1) Now, get rid of powers of 2 as they give even factors, so the remaining left out numbers would be (2+1)(2+1)=9 factors......................(2) All the remaining factors will be odd, therefore 3600 has 459= 36 even factors. Hence, the answer is D. Hope it helps. if you like.
Originally posted by topper97 on 19 Oct 2018, 08:20.
Last edited by topper97 on 04 Nov 2018, 05:36, edited 1 time in total.



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Re: How many factors of 3600 are even?
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19 Oct 2018, 08:40
Hi GMATinsightWhy cant we count normally ? Like 2^0(discarded) 2^1* any factor of 3/5 =1*6 2^2* any factor of 3/5 =1*6 2^3* any factor of 3/5 =1*6 2^4* any factor of 3/5 =1*6 total 24
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Re: How many factors of 3600 are even?
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19 Oct 2018, 08:58
ShankSouljaBoi wrote: Hi GMATinsightWhy cant we count normally ? Like 2^0(discarded) 2^1* any factor of 3/5 =1*6 2^2* any factor of 3/5 =1*6 2^3* any factor of 3/5 =1*6 2^4* any factor of 3/5 =1*6 total 24 ShankSouljaBoiWhat you are counting as 6 is actually 9 (Combination of all powers of 3 with all powers of 5) 2^1* any factor of 3/5 =1*9 2^2* any factor of 3/5 =1*9 2^3* any factor of 3/5 =1*9 2^4* any factor of 3/5 =1*9 Total = 36 I hope this helps!!!
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Re: How many factors of 3600 are even?
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05 Nov 2018, 22:36
Hi,
this was very helpful. Had a doubt though..so is there any way to directly figure the no of even factors? my question being why did we find the odd factors first and then substract from the total instead of directly finding the even?



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Re: How many factors of 3600 are even?
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06 Nov 2018, 01:24
Please scroll above. I have illustrated the same yashna36Posted from my mobile device
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Re: How many factors of 3600 are even?
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06 Nov 2018, 06:08
yashna36 wrote: Hi,
this was very helpful. Had a doubt though..so is there any way to directly figure the no of even factors? my question being why did we find the odd factors first and then substract from the total instead of directly finding the even? Your doubt is valid and one solution is posted above but think from this perspective Who would think that calculating even factors will be more difficult than calculating even factors???because a layman idea would be to consider calculation of both equally easy/tough therefore it's always good to know both methods. I hope this helps!!!
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Re: How many factors of 3600 are even? &nbs
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