gcd and addictive inverse?

Question

Find the greatest common divisor of 127, 39. And does 37 have an addictive inverse in Z127(lower base)

Answer 1

Let's factor both numbers.
39 = 3*13
127 is not divisible by 2, 3, 5, 7 or 11, so it's prime.
(The square root of 127 is a bit more than 11.)
So the GCD of 39 and 127 is 1.
Yes, 37 has an additive inverse in Z_127. It is 90,
since 37 + 90 = 0(mod 127).
Since 127 is prime, every nonzero number in Z_127
has a multiplicative inverse as well.

Answer 2

since the greatest no. which can divide both 127 & 39 is 1
therefore gcd of these numbers is 1