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# what is the greatest integer that will always evenly divide

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Intern
Joined: 22 Feb 2008
Posts: 5
what is the greatest integer that will always evenly divide  [#permalink]

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23 Feb 2008, 00:06
1
what is the greatest integer that will always evenly divide the sum of three consecutive even no.
a=2
b=3
c=4
d=6
e=12

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Director
Joined: 14 Jan 2007
Posts: 732

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23 Feb 2008, 05:48
My solution may not be elegant, but I got it quick.
IMO it's 6.

To find the greatest divisor of the sum of any three consecutive even numbers, think of the smallest set of three consecutive even numbers- 0, 2, 4
So it should be 6.
Current Student
Joined: 28 Dec 2004
Posts: 3203
Location: New York City
Schools: Wharton'11 HBS'12

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24 Feb 2008, 21:53
I get 6 as well..

took me sometime though..around 1 minute..

anyone got a shorter cut?
SVP
Joined: 29 Mar 2007
Posts: 2401

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27 Feb 2008, 08:35
das wrote:
what is the greatest integer that will always evenly divide the sum of three consecutive even no.
a=2
b=3
c=4
d=6
e=12

The lowest we can achieve here is 0,2,4. Thus 6. Try other evens to make sure these sets are also divisible by 6.

D

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Non-Human User
Joined: 09 Sep 2013
Posts: 10147
Re: what is the greatest integer that will always evenly divide  [#permalink]

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20 Feb 2019, 23:14
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Re: what is the greatest integer that will always evenly divide   [#permalink] 20 Feb 2019, 23:14
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