what is the greatest integer m for which the number 40 ! / 10 ^ m is an integer ?
"10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 40 ! the multiples of 5 are : 5 , 10 , 15 , 20 , 5 * 5 , 30 , 35 , 40 . thus 5 ^ 9 will divide 40 ! but 5 ^ 10 will not . clearly 2 ^ 9 will divide 40 ! so m = 9 is the largest possible integer . the answer is c ."
floor(divide(40, divide(10, const_2)))