最大公因數，也稱最大公約數、最大公因子，指兩個或多個整數共有約數中最大的一個.最大公約數有多種方法，常見的有質因數分解法，短除法，輾轉相除法，更相減損法.

[程式碼實現]

/*遞迴實現*/
#include<cstdio>
int GCD(int a,int b)
{
    return a%b?GCD(b,a%b):b;
}
int main()
{
    int x,y;
    scanf("%d%d",&x,&y);
    printf("%d",GCD(x,y));
    return 0;
}
 

/*非遞迴實現*/
#include<cstdio>
#include<cstdlib>
int x,y;
int gcd(int m,int n)
{
    int t;
    while (m%n!=0)
    {
        t=m%n;
      　m=n;
        n=t;
    }
　return n;
}
int main()
{
    scanf("%d %d",&x,&y);
    printf("%d",gcd(x,y));
    return 0;
}

#include <stdio.h>
int main() 
{
	int m, n; int m_cup, n_cup, res; /*被除數, 除數, 餘數*/ 
	printf("Enter two integer:\n"); 
	scanf("%d %d", &m, &n); 
	if (m > 0 && n >0) 
	{ 
		m_cup = m; 
		n_cup = n; 
		res = m_cup % n_cup; 
		while (res != 0) 
		{ 
			m_cup = n_cup; 
			n_cup = res; 
			res = m_cup % n_cup; 
		}
		printf("Greatest common divisor: %d\n", n_cup); 
		printf("Lease common multiple : %d\n", m * n / n_cup); 
   } 
  else printf("Error!\n"); 
  return 0; 
}