If n is a positive integer, n! is the product of the first n positive integers. For example, 4! = 4 x 3 x 2 x 1 =24. If u and v are positive integers and u!=v! x 53, then v could equal

Question

If n is a positive integer, n! is the product of the first n positive integers. For example, 4! = 4 x 3 x 2 x 1 =24. If u and v are positive integers and u!=v! x 53, then v could equal 
A. 6
B. 8
C. 56
D. 57

Steve · Answer

53 is a prime, so it cannot appear in any factorial less than 53! I don't see how v can be anything other than 52, but that's not one of the choices. Hmmmm...