If a, b, and c are three positive integers, each greater than 1, what is the remainder when the product abc is divided by 2?
(1) If each of a, b, and c is divided by 2, the product of all three remainders is 0.
(2) If each of a, b, and c is divided by 2, the sum of all three remainders is 2.
(1) If each of a, b, and c is divided by 2, the product of all three remainders is 0.
(2) If each of a, b, and c is divided by 2, the sum of all three remainders is 2.