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? Choose the most appropriate option:  A) 10  B) 12  C) 14  D) 16  E) 18
No need to actually find the product of 1 to 30. Just look at the numbers that have factors of 3.   3 = 3   6 = 3 * 2   9 = 3 * 3   12 = 3 * 2 * 2   15 = 3 * 5   18 = 3 * 3 * 2   21 = 3 * 7   24 = 3 * 2 * 2 * 2   27 = 3 * 3 * 3   30 = 3 * 2 * 5   There are 14 3's, so the largest factor of p for 3k is 3*14   ANSWER:14
<result>C</result>
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?