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If p is the product of the integers from 1 to 30, inclusive, [#permalink]
 17 Jul 2008, 02:55
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 Show the quickest way to solve this.
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Re: Math Set 1: Q15 [#permalink]
17 Jul 2008, 03:58
jimmylow wrote: 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
Show the quickest way to solve this. C Since 3 is a prime number, the numbers 1 to 30 that are relevant here are only numbers with 3 as a factor, i.e., multiples of 3: 3, 6, 9...27, 30 3 numbers have 3 as a factor multiple times: 9, 18, 27. 7 have 3 as a factor only once. 9 = 3^2 18 = 2*3^2 27 = 3^3 Counting up: 7+2+2+3 = 14
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Re: Math Set 1: Q15 [#permalink]
06 Aug 2008, 17:52
jimmylow wrote: 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
Show the quickest way to solve this. Fastest way to solve: 30/3 = 1010/3 = 3 (with a remainder) 3/3 = 1Then just add up the quotients: 10 + 3 + 1 = 14 C 
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Re: Math Set 1: Q15 [#permalink]
06 Aug 2008, 19:12
jimmylow wrote: 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
Show the quickest way to solve this. 3,6,9,12,15,18,21,24,27,30 -------> total is 14 => k=14 can be the highest power of 3 to make 3^k a divisor of p
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cheers
Its Now Or Never
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Re: Math Set 1: Q15
[#permalink]
06 Aug 2008, 19:12
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