If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?
Select the correct option:  A) 7  B) 8  C) 9  D) 10  E) 11
The factors of 10 are 1, 2, 5, and 10.   To find what k is, find how many times you can make 10 with the numbers in 1-40.   First, find the 10's as they are going to be most restrictive. Only 10, 20, 30 and 40 have 10 as a factor. 4 total.   Next find 5's. 5, 15, 25 and 35 each have a 5, with 25 having 2. 5 total.   You don't need to find the twos as you know there are more than 5's.   Add the two you get 9.   ANSWER:9
<result>C</result>
If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?