If n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2^k is a factor of n?
.
Select:
A) 10
B) 12
C) 15
D) 18
E) 20
20! = 1*2*3*4*5...*19*20 (This is 20 factorial written as 20!)   n = 1*2*3*4*5*6*7.....*19*20   How many 2s are there in n?   One 2 from 2   Two 2s from 4   One two from 6   Three 2s from 8   and so on...   When you count them all, you get 18.   ANSWER:18
<result>D</result>
If n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2^k is a factor of n?
.