For nonzero integers, a, b, prove the following properties of divisibility and gcds. (you may use the fact that gcd(a, b) is an integer linear combination of a and b. you may not appeal to uniqueness of prime factorization because the properties below are needed to prove unique factorization.) (a) every common divisor of a and b divides gcd(a, b). (b) if a | bc and gcd(a, b) = 1, then a | c.