Euclidean algorithm for greatest common divisor (GCD)

The greatest common divisor algorithm for Euclidean algorithm,

The code is as follows:

int gcd (int a, int b) {if (b = = 0) return A; else gcd (b, a% b  

Prove:

For a, B, there is a = kb + R (A, K, B, r are integers), where r = a mod B.

Make d A and b a convention number, then d|a,d|b (i.e. A, b are evenly divisible by D),

So R =a-kb, both sides divided by D.

R/D = A/D-kb/d = m (M is an integer, because R is also divisible by D)

So I know

The number of conventions and B, a mod b conventions are the same, so they greatest common divisor the same.

That is gcd (A, b) = gcd (b, R)

When r=0, B is obviously (B,R) greatest common divisor, that is, the greatest common divisor of a B,

Euclidean algorithm for greatest common divisor (GCD)