what is the greatest integer m for which the number 30 ! / 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 30 ! the multiples of 5 are : 5 , 10 , 15 , 20 , 5 * 5 , 30 . thus 5 ^ 7 will divide 30 ! but 5 ^ 8 will not . clearly 2 ^ 7 will divide 30 ! so m = 7 is the largest possible integer . the answer is a ."
floor(divide(30, divide(10, const_2)))