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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Product of integers problem
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Stuart@KaplanGMAT
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Brute force is the way to go.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
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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x2suresh
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30/3 = 10jfranco23 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
30/3^2 ~ 3.
30/3^3 ~ 1
Ans = 10+3+1 =14
