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If p is the product of the integers from 1 to 30, inclusive, [#permalink]
 01 Oct 2005, 06:16
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If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18
Last edited by mbassmbass04 on 01 Oct 2005, 07:55, edited 1 time in total.
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Current Student
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There must be a simple formula for calculating 1*2*3*4.....30 but I don`t know it. Any hints???
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Current Student
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1*2*3*4....18*....30/3(18)
Both the 3 and the 18 cancel out.
E.
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Manager
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ETS loves similar question, they call it Logic questions
Let's count the factors of 3 that exists between 1 and 30
3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12
3 x 5 = 15
3 x 3 x 2 = 18
3 x 7= 21
3 x 8= 24
3 x 3 x 3 = 27
3 x 10 = 30
There are 14 factors of 3, Answer is 14
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SVP
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mbassmbass04 wrote: ETS loves similar question, they call it Logic questions. Let's count the factors of 3 that exists between 1 and 30
3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12
3 x 5 = 15
3 x 3 x 2 = 18
3 x 7= 21
3 x 8= 24
3 x 3 x 3 = 27
3 x 10 = 30
There are 14 factors of 3, Answer is 14
then 3k should be updated as 3^k. as it is 18 is the answer however it is not the correct one......
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Manager
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Yes, you are totally right, I will update it.
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Manager
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Simple formula
= [30/3] + [30/(3^2)] + [30/(3^3)]
= 10 + 3 + 1
= 14
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