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# How many distinct prime factors do 4! and 8! have in common?

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Manager
Joined: 18 Aug 2005
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Location: Italy, Rome caput mundi
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How many distinct prime factors do 4! and 8! have in common? [#permalink]  27 Sep 2005, 03:13
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50% (01:51) correct 50% (00:21) wrong based on 1 sessions
How many distinct prime factors do 4! and 8! have in common?

4

3

2

1

0
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Current Student
Joined: 29 Jan 2005
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C. 2 and 3. 8!= 40320 and 4!=24. Only 2 and 3 divide evenly into both numbers. Probably easier to work with the smaller number first in this example.
Manager
Joined: 06 Aug 2005
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You should not be working out 4! and 8! in this sort of question.

4! = 1 * 2 * 3 * 4
8! = 4! * 5 * 6 * 7 * 8

So the answer can only be a factor of 4!.
1 is irrelevant.
4 = 2^2.
So the answer is 2 and 3.
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