gcd questions (fairly simple)

I feel like these are stupid questions but I just want to double check myself. (also would i have to show some sort of proof/explanation for my answers?)

(a) Let a be a positive integer. What is the greatest common divisor of a and a^2? This would be a right? With the idea of if a is a prime number than obviously the only divisor is going to be 1 and itself.

(b) Let a be a positive integer. What is the greatest common divisor of a and a+2? Would this be 1 if a is odd and 2 if a is even?

(c) show that if a and be are integers with (a,b)=1, then (a+b,a-b)=1 or 2.