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How many factors greater than 1 do 12000, 21000, and 27000 have in com

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Joined: 03 Jul 2013
Posts: 38
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How many factors greater than 1 do 12000, 21000, and 27000 have in com  [#permalink]

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New post 25 Jan 2016, 23:25
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (02:08) correct 42% (02:49) wrong based on 55 sessions

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How many factors greater than 1 do 12000, 21000, and 27000 have in common?

(A) 18
(B) 31
(C)16
(D 27
(E) 30

source: self made
N.B it is self made question so may have any flaws in construction :oops:
Math Expert
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Joined: 02 Aug 2009
Posts: 7556
Re: How many factors greater than 1 do 12000, 21000, and 27000 have in com  [#permalink]

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New post 26 Jan 2016, 00:07
shiblee wrote:
How many factors greater than 1 do 12000, 21000, and 27000 have in common?

(A) 18
(B) 31
(C)16
(D 27
(E) 30

source: self made
N.B it is self made question so may have any flaws in construction :oops:


Hi,
the Q seems to be absolutely correct...
And since you have made the Q, I believe you know the answer/solution..

For others..
this Q basically wants us to find the HCF, as there will be no integer greter than HCF which could divide evenly into all three numbers..
the number of factors will be the number of factors of HCF..

HCF of 12000, 21000, and 27000 will be 3000..
the number of factors of 3000:-
3000=2^3*3*5^3..
so factors=(3+1)(1+1)(3+1)=32..
32 includes 1.. so apart from =32-1=31..
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Re: How many factors greater than 1 do 12000, 21000, and 27000 have in com  [#permalink]

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New post 26 Jul 2017, 10:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many factors greater than 1 do 12000, 21000, and 27000 have in com   [#permalink] 26 Jul 2017, 10:55
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How many factors greater than 1 do 12000, 21000, and 27000 have in com

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