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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: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

How many integers are divisible by 4 are there between 8! [#permalink]  24 Dec 2007, 06:54
How many integers are divisible by 4 are there between 8! and 8!+20 inclusive?
Director
Joined: 12 Jul 2007
Posts: 864
Followers: 13

Kudos [?]: 224 [0], given: 0

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: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

very nice.

just wanted to double check my work.
Director
Joined: 03 Sep 2006
Posts: 884
Followers: 6

Kudos [?]: 290 [0], given: 33

Re: factorial divisibility [#permalink]  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.
Re: factorial divisibility   [#permalink] 24 Dec 2007, 07:17
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