So, in the image, we have the definition of the GCD. The only part of the text I don't understand is when it says that the set of common divisors is bounded above by the largest of $a$, $b$, $-a$, $-b$. I don't understand the reference to "$-a$, $-b$" ? I thought that the two numbers $a$ and $b$ are always positive, so what gives ? Thank you for the help !
The text says:
If you have two numbers $a=-9$ and $b=-3$, a common divisor cannot be bigger than $\max \{a,b,-a,-b \} = \max \{-9,-3,9,3 \} = 9$.
So, all common divisors are $\leq 9$ which leads to the greatest common divisor exists and it is unique.