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Director  V
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How many factors of 9600 are not divisible by 12?  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 51% (02:10) correct 49% (02:32) wrong based on 220 sessions

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How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42

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Manish "Only I can change my life. No one can do it for me"
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How many factors of 9600 are not divisible by 12?  [#permalink]

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CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42

Let's write 9600 in prime factorization form, 9600=$$2^7$$*$$5^2$$*$$3^1$$

Hence the no of factors of 9600=(7+1)(2+1)(1+1)=8*3*2=48

The no factors of 9600 not divisible by 12=Total of no factors of 9600- Total no of factors of 9600 which are divisible by 12

Now we can write, 9600=$$2^7$$*$$5^2$$*$$3^1$$=$$2^2$$*3($$2^5$$*$$5^2$$)=12($$2^5$$*$$5^2$$)

Since 12($$2^5$$*$$5^2$$) is multiple of 12, hence the no of factors which are divisible by 12 =(5+1)(2+1)=6*3=18

Therefore,the no factors of 9600 not divisible by 12=48-18=30

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Originally posted by PKN on 05 Jun 2018, 23:16.
Last edited by PKN on 08 Jun 2018, 18:48, edited 1 time in total.
##### General Discussion
Director  V
Joined: 12 Feb 2015
Posts: 957
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12

To find the number of factors of 9600 that are divisible by 12 is a straightforward application of number of factors formula & some LOGIC:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]

9600 could be written as 12 * 800
Now 10 is a factor of 800, so is 20, so is 400, including many others.
10, 20 and 400 are not divisible by 12 but (12*10), (12*20) and (12*400) are divisible by 12 because we are multiplying and dividing my 12. Hence every factor of 800 is also a factor of 9600 and is divisible by 12 if we are multiplying each factor of 800 by 12.

To find the number of factors of 800 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]

Therefore 800 can be written as $$2^5∗5^2$$
Therefore the number of factors of 800 are (5+1)(2+1) = 6*3 = 18 factors.

All the factors of 800 are also the factors of 9600 that are divisible by 12 because as per our LOGIC we are multiplying each factor of 800 by 12. Therefore the no. of factors of 9600 that are divisible by 12 is also 18 factors.

Please revert in case if you need more clarification!!
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Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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9600 could be written as 12 * 800
Now 10 is a factor of 800, so is 20, so is 400, including many others.
10, 20 and 400 are not divisible by 12 but (12*10), (12*20) and (12*400) are divisible by 12 because we are multiplying and dividing my 12. Hence every factor of 800 is also a factor of 9600 and is divisible by 12 if we are multiplying each factor of 800 by 12.

To find the number of factors of 800 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]

Therefore 800 can be written as $$2^5∗5^2$$
Therefore the number of factors of 800 are (5+1)(2+1) = 6*3 = 18 factors.

Therefore the no. of factors of 9600 which are divisible by 12 are 18 factors in total.

But the question stem asks us how many factors of 9600 are NOT divisible by 12?

Therefore we will have to deduct all the factors of 9600 which are divisible by 12 from all the factors of 9600 to get all the factors of 9600 which are NOT divisible by 12.

9600 can be written as $$2^7∗3*5^2$$
Therefore the number of factors of 9600 are (7+1)(1+1)(2+1) = 8*2*3 = 48 factors.

All the factors of 9600 which are NOT divisible by 12 = 48 factors - 18 factors = 30 factors [hence the correct answer is (B)]
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Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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can someone please explain how the get factors of 9600 divisible by 12
Director  V
Joined: 12 Feb 2015
Posts: 957
Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12

For practice:-

https://gmatclub.com/forum/how-many-fac ... 66709.html

https://gmatclub.com/forum/how-many-fac ... 67283.html
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Manish "Only I can change my life. No one can do it for me"
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Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12

Another method just to lay a strong foundation on how to use the formula using another logic but not advisable to use it in GMAT as this method is time consuming:-

https://gmatclub.com/forum/how-many-fac ... l#p2072897
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Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42

Let’s first determine the total number of factors of 9600. We express 9600 as a product of primes. We add 1 to each prime’s exponent, and then find the product of those numbers.

9600 = 96 x 100 = 16 x 6 x 5^2 x 2^2 = 2^4 x 2 x 3 x 5^2 x 2^2 = 2^7 x 3 x 5^2

So the total number of factors of 9600 is (7 + 1)(1 + 1)(2 + 1) = 48.

9600 = 12 x 800

To determine how many factors ARE divisible by 12, we can break 800 into primes and determine the total number of factors of 800.

800 = 8 x 100 = 2^3 x 2^2 x 5^2 = 2^5 x 5^2

So 800 has (5 + 1)(2 + 1) = 18

Thus, the number of factors of 9600 that are not divisible by 12 are 48 - 18 = 30.

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Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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PKN wrote:
CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42

Let's write 9600 in prime factorization form, 9600=$$2^7$$*$$5^2$$*$$3^1$$

Hence the no of factors of 9600=(7+1)(2+1)(1+1)=8*3*2=48

The no factors of 9600 not divisible by 12=Total of no factors of 9600- Total no of factors of 9600 which are divisible by 12

Now we can write, 9600=$$2^7$$*$$5^2$$*$$3^1$$=$$2^2$$*3($$2^5$$*$$5^2$$)=12($$2^5$$*$$5^2$$)

Since $$2^5$$*$$5^2$$ is multiple of 12, hence the no of factors which are divisible by 12 =(5+1)(2+1)=6*3=18

Therefore,the no factors of 9600 not divisible by 12=48-18=30

2^5*5^2 is a multiple of 12 ?
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Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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avijit02 wrote:
PKN wrote:
CAMANISHPARMAR wrote:
How many factors of 9600 are not divisible by 12?

A) 48
B) 30
C) 24
D) 20
E) 42

Let's write 9600 in prime factorization form, 9600=$$2^7$$*$$5^2$$*$$3^1$$

Hence the no of factors of 9600=(7+1)(2+1)(1+1)=8*3*2=48

The no factors of 9600 not divisible by 12=Total of no factors of 9600- Total no of factors of 9600 which are divisible by 12

Now we can write, 9600=$$2^7$$*$$5^2$$*$$3^1$$=$$2^2$$*3($$2^5$$*$$5^2$$)=12($$2^5$$*$$5^2$$)

Since $$2^5$$*$$5^2$$ is multiple of 12, hence the no of factors which are divisible by 12 =(5+1)(2+1)=6*3=18

Therefore,the no factors of 9600 not divisible by 12=48-18=30

2^5*5^2 is a multiple of 12 ?

Hi avijit02,

Typo error edited. Thanks
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Re: How many factors of 9600 are not divisible by 12?  [#permalink]

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Meghakothari98 wrote:
can someone please explain how the get factors of 9600 divisible by 12

9600=2^7*3*5^2
total factors of 9600=(7+1)(1+1)(2+1)=8*2*3=48
since we want to find factors of 12
write 9600 as a multiple of 12
now 9600=(2^2*3)(2^5*5^2)=12(2^5*5^2)
now factors of 9600 divisible by 12=(5+1)(2+1)=6*3=18
now from here we can find factors of 9600 not divisible by 12
=total factors of 9600-factors of 9600 divisible by 12
=48-18=30 Re: How many factors of 9600 are not divisible by 12?   [#permalink] 26 Jun 2018, 03:47
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