Answer
the algorithm finds that gcd(8, 13) = 1.
Work Step by Step
With the given input,
-- the algorithm uses the else clause to find that
gcd(8, 13) = gcd(13 mod 8, 8) = gcd(5, 8).
-It uses this clause again to find that
gcd(5, 8) = gcd(8 mod 5, 5) = gcd(3, 5),
- then to get gcd(3, 5) = gcd(5 mod 3, 3) = gcd(2, 3),
then gcd(2, 3) = gcd(3 mod 2, 2) = gcd(1, 2),
and once more to get
- gcd(1, 2) = gcd(2 mod 1, 1) = gcd(0, 1).
--Finally, to find gcd(0, 1) it uses the first step with a = 0 to find that gcd(0, 1) = 1.
- Consequently,
-the algorithm finds that gcd(8, 13) = 1.
