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pattydread
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what is the largest integer value of x that makes 30!/3^x an 19 Aug 2008, 08:33
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what is the largest integer value of x that makes 30!/3^x an integer?

10

12

14

16

18



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nmohindru
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what is the largest integer value of x that makes 30!/3^x an 19 Aug 2008, 08:37
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pattydread
what is the largest integer value of x that makes 30!/3^x an integer?

10

12

14

16

18
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30! is multiple of 30, 27, 24, 21, 18, 15, 12, 9, 6, 3 = \(3*3^3*3*3*3^2*3*3*3^2*3*3 = 3 ^ 14\)

Therefore answer is 14
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x2suresh
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what is the largest integer value of x that makes 30!/3^x an 19 Aug 2008, 14:21
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pattydread
what is the largest integer value of x that makes 30!/3^x an integer?

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\(30/3 + 30/3^2(nearest integer) + 30/3^3 (nearest integer)\)
= 10+3 +1=14
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bigtreezl
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what is the largest integer value of x that makes 30!/3^x an 19 Aug 2008, 15:30
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can someone please add an explanation with more detail?
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Nerdboy
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what is the largest integer value of x that makes 30!/3^x an Updated on: 20 Aug 2008, 23:00
Originally posted by Nerdboy on 20 Aug 2008, 01:35.
Last edited by Nerdboy on 20 Aug 2008, 23:00, edited 1 time in total.
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bigtreezl
can someone please add an explanation with more detail?
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This is the same problem as this one:
7-t69074

So, we have to count the 3's in 30!. This is done like x2suresh did: 10 numbers have at least one 3, 3 numbers have one additional 3 each, and one number (27) has yet one more 3. Which makes 14.
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bigtreezl
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what is the largest integer value of x that makes 30!/3^x an 20 Aug 2008, 10:08
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ok..i get it now..thanks nerdboy



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