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Number properties problem

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by Troika » Mon Apr 09, 2012 5:51 pm
If p is the product of 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

OA: C

Source: OG 12, #110
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by GMATGuruNY » Mon Apr 09, 2012 6:38 pm
I posted a solution here:

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by pemdas » Mon Apr 09, 2012 6:42 pm
p=30! and in there select 3,6,9,12,15,18,21,24,27,30 all the multiples of 3. Then rewrite them as the primes 3,3*2,3*3,3*2*2,3*5,3*3*2,3*7,3*2*2*2,3*3*3,3*2*5. If you noticed we have exactly 14 repeating 3s, hence the greatest factor of p will be 3^k where k=14

c
HG10 wrote:If p is the product of 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

OA: C

Source: OG 12, #110
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by Troika » Tue Apr 10, 2012 5:34 pm
@GMATGuruNY & pemdas: thank you for the solutions!
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