Stein algorithm computes GCD using only subtraction and shifts, no division. It is faster on some hardware.
Idea: if both a and b are even, gcd(a, b) = 2 × gcd(a/2, b/2). If a is even and b is odd, gcd(a, b) = gcd(a/2, b). If both odd, gcd(a, b) = gcd(a - b, b).
This avoids slow division on processors without hardware dividers. You will rarely code this by hand, but know it exists.