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

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CEO
Joined: 21 Jan 2007
Posts: 2747
Location: New York City
Followers: 11

Kudos [?]: 941 [0], given: 4

How many integers are divisible by 4 are there between 8! [#permalink]

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24 Dec 2007, 07:54
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?
Director
Joined: 12 Jul 2007
Posts: 861
Followers: 17

Kudos [?]: 307 [0], given: 0

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24 Dec 2007, 08:07
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.
CEO
Joined: 21 Jan 2007
Posts: 2747
Location: New York City
Followers: 11

Kudos [?]: 941 [0], given: 4

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24 Dec 2007, 08:10
very nice.

just wanted to double check my work.
Director
Joined: 03 Sep 2006
Posts: 875
Followers: 7

Kudos [?]: 893 [0], given: 33

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24 Dec 2007, 08:17
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.
Re: factorial divisibility   [#permalink] 24 Dec 2007, 08:17
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