Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=36, what is the maximum value of y for which f(x,y)=0?
Choose the correct choice from the following answers: A) 9 B) 12 C) 18 D) 20 E) 30

Rationale: "the question is finding y such that ( 36 - y ) ! is a multiple of 36 . that means we need to have 2 ^ 2 * 3 ^ 2 in ( 36 - y ) ! 6 ! is the smallest factorial number with 2 ^ 2 * 3 ^ 2 as a factor . 36 - y = 6 y = 30 the answer is e ."
Answer: E