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# 12! /2^M is an integer.. whats the maximum value of M?

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CEO
Joined: 15 Aug 2003
Posts: 3452

Kudos [?]: 925 [0], given: 781

12! /2^M is an integer.. whats the maximum value of M?  [#permalink]

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09 Oct 2003, 16:30
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12! /2^M is an integer.. whats the maximum value of M?

EDIT : " MAXIMUM VALUE"

Last edited by Praetorian on 09 Oct 2003, 18:08, edited 1 time in total.

Kudos [?]: 925 [0], given: 781

Manager
Joined: 26 Aug 2003
Posts: 232

Kudos [?]: 13 [0], given: 0

Location: United States

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09 Oct 2003, 17:37
M = 10?

Count the number of 2's that can go into all the even numbers, leaving prime factors, in 12!

Kudos [?]: 13 [0], given: 0

SVP
Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 308 [0], given: 0

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14 Oct 2003, 01:45
12! includes:

numbers divisible by 2) 6 items
numbers divisible by 4) 3 items
numbers divisible by 8) 1 item

6+3+1=10, so 2^10 is a maximal power of 2 that 12! contains.

Kudos [?]: 308 [0], given: 0

14 Oct 2003, 01:45
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# 12! /2^M is an integer.. whats the maximum value of M?

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