We consider common
divisors and multiples of two (or more) integers.
Let a, b 
Z.
Definition
- An integer d is a common divisor of a and b if d | a and d | b .
- If a and b are not both zero, the largest common divisor of a and b (exists and) is called the greatest common divisor of a and b.
- If the greatest common divisor of a and b equals 1, then a and b are called relatively prime.
We denote the greatest common divisor of a and b by gcd(a,b).
Analogous to the greatest common divisor of two integers we can define the greatest common divisor of more than two numbers.
Euclid's famous algorithm for calculating a greatest common divisor will be discussed later.