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How many factors of 3600 are even?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 60% (01:33) correct 40% (01:33) wrong based on 134 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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Math Expert V
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Posts: 7984
Re: How many factors of 3600 are even?  [#permalink]

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5
3
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 = 45-9=36

D

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Re: How many factors of 3600 are even?  [#permalink]

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2
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 = 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

I hope this helps!

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Re: How many factors of 3600 are even?  [#permalink]

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GMATinsight wrote:
How many factors of 3600 are even?

A) 9
B) 12
C) 24
D) 36
E) 45

Source: http://www.GMATinsight.com

Prime 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
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How many factors of 3600 are even?  [#permalink]

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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 45-9=36 even factors.

Hence, the answer is D.

Hope it helps. if you like.
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Originally posted by EncounterGMAT on 19 Oct 2018, 09:20.
Last edited by EncounterGMAT on 04 Nov 2018, 06:36, edited 1 time in total.
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Re: How many factors of 3600 are even?  [#permalink]

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Hi GMATinsight
Why 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?  [#permalink]

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ShankSouljaBoi wrote:
Hi GMATinsight
Why 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

ShankSouljaBoi
What 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?  [#permalink]

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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?  [#permalink]

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Please scroll above. I have illustrated the same yashna36

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Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

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Re: How many factors of 3600 are even?  [#permalink]

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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?  [#permalink]

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GMATinsight wrote:
How many factors of 3600 are even?

A) 9
B) 12
C) 24
D) 36
E) 45

Source: http://www.GMATinsight.com

Alternative:

3600 = 2*1800

i.e. every factor of 1800 when multiplied with 2 will become even factor of 3600

$$1800 = 2^3*3^2*5^2$$

factors of $$1800 = (3+1)*(2+1)*(2+1) = 4*3*3 = 36$$

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ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Re: How many factors of 3600 are even?   [#permalink] 17 Feb 2019, 08:48
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