Write a complete mathematical definition of (a, b), the greatest common divisor of a, b in \mathbb{z}

The greatest common divisor of two integers a and b (not both 0) is the largest integer that divides both a and b.

Step-by-step explanation:

Think for example of the numbers a=5, and b= -10. The greatest common divisor of 5 and -10, is the largest integer that divides both 5 and -10. We can find it by inspection (although there are more advanced methods to find it). We can list all integers that divide both 5 and -10.

-5 divides 5, and it also divides -10

-1 divides 5, and it also divides -10

1 divides 5, and it also divides -10

5 divides 5, and it also dividies -10

The LARGEST of them all is then 5, so 5 is the greatest common divisor of 5 and -10. The usual way to write it is