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How many integers are divisible by 4 are there between 8!

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CEO
CEO
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Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1091 [0], given: 4

Location: New York City
How many integers are divisible by 4 are there between 8! [#permalink]

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New post 24 Dec 2007, 06:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many integers are divisible by 4 are there between 8! and 8!+20 inclusive?

Kudos [?]: 1091 [0], given: 4

Director
Director
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Joined: 12 Jul 2007
Posts: 857

Kudos [?]: 341 [0], given: 0

 [#permalink]

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New post 24 Dec 2007, 07:07
We know 8! is divisible by 4 because 8! = 8*7*6*5*4*3*2*1

so 8! +4, +8, +12, +16, +20 are all divisible by 4 as well. Giving us 6 integers as our answer.

Kudos [?]: 341 [0], given: 0

CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1091 [0], given: 4

Location: New York City
 [#permalink]

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New post 24 Dec 2007, 07:10
very nice. :lol:

just wanted to double check my work.

Kudos [?]: 1091 [0], given: 4

Director
Director
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Joined: 03 Sep 2006
Posts: 862

Kudos [?]: 1128 [0], given: 33

GMAT ToolKit User
Re: factorial divisibility [#permalink]

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New post 24 Dec 2007, 07:17
bmwhype2 wrote:
How many integers are divisible by 4 are there between 8! and 8!+20 inclusive?



8!+20 - 8! = 20/4 =5

Thus 5 integers.

Now check the last one...8!+20...which is also divisible by 4

Thus 5+1 = 6 integers.

Kudos [?]: 1128 [0], given: 33

Re: factorial divisibility   [#permalink] 24 Dec 2007, 07:17
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How many integers are divisible by 4 are there between 8!

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