Euclidean algorithm for GCD in C# By CodeAgha

description.txt

 Euclidean algorithm for GCD in C# By CodeAgha
    The parenthesis is the GCD (Greatest common factor) sign and the 'mod' symbol is equal to the remainder of the division.
    In any case, we write the smaller number first and the larger number second

    Proof from division theorem

    a/b => a = bq + r

    v != 0 | gcd(u, v) = gcd(v, u mod v) 

    gcd(u, u) = u
    gcd(u, 0) = |u|
    

    - examples : 
        gcd(12, 30) = gcd(12, 30 mod 12) = gcd(6, 12) = gcd(6, 12 mod 6) = gcd(6, 6) = 6
        gcd(18, 48) = gcd(18, 48 mod 18) = gcd(12, 18) = gcd(12, 18 mod 12) = gcd(6, 12) = gcd(6 , 12 mod 6) = gcd(6, 6) = 6
        gcd(9, 24) = gcd(9, 24 mod 9) = gcd(6, 9) = gcd(6, 9 mod 6) = gcd(3, 6) = gcd(3, 6 mod 3) = gcd(3, 0) = |3| = 3
 

euclidean-gcd.cs

// long and simple write :
int gcd(int u, int v)
{
    if (v != 0)
    {
        return gcd(v, u % v);
    }
    return u;
}

// short and complex write :
int gcd(int u, int v) => ((v != 0) ? gcd(v, u % v) : u);

euclidean-gcd.py

def gcd(u,v):
  return gcd(v, u % v) if (v != 0) else u