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Product of integers problem

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Product of integers problem

by jfranco23 » Thu Feb 12, 2009 12:03 pm
Hi, i need help with this problem, thanks

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
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Re: Product of integers problem

by Stuart@KaplanGMAT » Thu Feb 12, 2009 12:15 pm
jfranco23 wrote:Hi, i need help with this problem, thanks

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
Brute force is the way to go.

The question is asking how many "3"s we can take out of 30!

Sources of single 3s: 3, 6, 12, 15, 21, 24, 30 = 7 3s
Sources of double 3s: 9, 18 = 4 3s
Source of triple 3: 27 = 3 3s

7 + 4 + 3 = 14 3s are factors of 30!... choose (C).
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Re: Product of integers problem

by x2suresh » Thu Feb 12, 2009 1:25 pm
jfranco23 wrote:Hi, i need help with this problem, thanks

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
30/3 = 10
30/3^2 ~ 3.
30/3^3 ~ 1

Ans = 10+3+1 =14
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