n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1600, then what is the smallest possible value of n? Choose the correct choice from the following answers:  A) 6  B) 8  C) 10  D) 12  E) 15
1600=2^6*5^2   2^6 means that n must be at least 8. That is, we need 2, 2*2, 6, and 2*2*2.   5^2 means that n must be at least 10. That is, We need 5 and 10.   The answer is 10.
<result>C</result>
n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1600, then what is the smallest possible value of n?