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
Please provide your answer with step-by-step explanation.
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Verified answer
Listing out the numbers to be multiplied:
No. No of 3's contained
1...............0
2...............0
3...............1
4...............0
5...............0
6...............1
7...............0
8...............0
9...............2
10.............0
11.............0
12.............1
13.............0
14.............0
15.............1
16.............0
17.............0
18.............2
19.............0
20.............0
21.............1
22.............0
23.............0
24.............1
25.............0
26.............0
27.............3
28.............0
29.............0
30.............1
Total 3's = 14 so answer is C.14