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what is the greatest integer that will always evenly divide

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what is the greatest integer that will always evenly divide [#permalink] New post 23 Feb 2008, 00:06
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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Re: integers [#permalink] New post 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.
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Re: integers [#permalink] New post 24 Feb 2008, 21:53
I get 6 as well..

took me sometime though..around 1 minute..

anyone got a shorter cut?
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Re: integers [#permalink] New post 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
Re: integers   [#permalink] 27 Feb 2008, 08:35
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