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# If 15!/3^m is an integer, what is the greatest possible

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Intern
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If 15!/3^m is an integer, what is the greatest possible [#permalink]

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27 Nov 2005, 19:08
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If 15!/3^m is an integer, what is the greatest possible value of m?

A 4
B 5
C 6
D 7
E 8

Can someone also give explaination on how they get the answer? Thanks...
SVP
Joined: 24 Sep 2005
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27 Nov 2005, 19:18
faisalt wrote:
If 15!/3^m is an integer, what is the greatest possible value of m?

A 4
B 5
C 6
D 7
E 8

Can someone also give explaination on how they get the answer? Thanks...

15!/3^m is an integer -----> 3^m is a factor of 15!
15: 3 = 5
5: 3 = 1
2: 3 = 0

15! has 3^ 6 (=1+5) as a factor ---> biggest m = 6
Director
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27 Nov 2005, 19:26
15 / 3 = 5
15 / 3^2 = 1
15 / 3^3 = 0

Thus, there are 6 3's in 15!.

The mamimum value of m is 6.
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VP
Joined: 06 Jun 2004
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27 Nov 2005, 21:21
I got 6 as well.

15/3 = 5
5/3 = 1
1/3 = 0

TOTAL = 6

Or you can write out all the factors of 15!

15*14*13*12*11*10*9...........1
(3*5)*14*13*(3*4)*11*10*(3*3)..........etc.
Senior Manager
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30 Nov 2005, 08:33
!15/3^m

(1) 15/3=5

(2) 5/3=1 2/3

3^m=3^5+1=3^6 So, m=6
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Director
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30 Nov 2005, 08:37
Factors of 15 in 15! =

15, 12, 9, 6, 3

Of that 9 = 3 * 3
So total 6
30 Nov 2005, 08:37
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