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# How many positive divisor of 192 are also multiples of 6

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Current Student
Joined: 28 Dec 2004
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Location: New York City
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Kudos [?]: 181 [0], given: 2

How many positive divisor of 192 are also multiples of 6 [#permalink]  19 Feb 2005, 18:43
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How many positive divisor of 192 are also multiples of 6?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

192 = 2*96
= 2*3*32
= 2*3*4*8
= 2*2*2*2*2*2*3
= 6(2*2*2*2*2)

Number of multiples: 6
Manager
Joined: 19 Nov 2004
Posts: 59
Followers: 1

Kudos [?]: 3 [0], given: 0

Do we consider 192 to be divisor of itself, and 6 multiple of 6?
If yes then 6, if no then 4
Director
Joined: 31 Aug 2004
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Kudos [?]: 43 [0], given: 0

Lovely : yes we do the answer is 6, best way is ywilfred's method.
Intern
Joined: 11 Dec 2003
Posts: 49
Location: IN
Followers: 1

Kudos [?]: 6 [0], given: 0

ywilfred wrote:
192 = 2*96
= 2*3*32
= 2*3*4*8
= 2*2*2*2*2*2*3
= 6(2*2*2*2*2)

Number of multiples: 6

I am missing something here could you please explain how you get
= 6(2*2*2*2*2) ?
isn't it "7" since 2*2*2*2*2*2*3 has "7" positive divisors which are also multiples of 6.

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

192 can be prime factorized into: 2*2*2*2*2*2*3. But we want to see how many multiples of 6. In order to get see that easily, we can combine one of the 2 and 3 to get a 6.
Thus we have 6(2*2*2*2*2). So now we know there are 5 multiples of 6 (from the five 2s'). But we must also count in the number 6 by itself since that's a multiple of 1.
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 5 [0], given: 0

Yup 6 it is same way just do prime factorization.
Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
Followers: 1

Kudos [?]: 5 [0], given: 0

An interesting thing [#permalink]  25 Feb 2005, 12:54
Do you know any even number greater than 2 can be written as the sum of two prime numbers (same or different)
An interesting thing   [#permalink] 25 Feb 2005, 12:54
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