C++求最大公约数四种方法解析

#include <iostream>
using namespace std;
int CommFactor1(int m, int n); //函数的声明
int main()
{
 int a, b;
 cin >> a >> b;
 cout << "这两个数的最大公约数为：" << CommFactor1(a,b)<< endl;
 return 0;
}
int CommFactor1(int m,int n)
{
 int tem;
 for (tem = m;; tem--)
 {
 if (m % tem == 0 && n % tem == 0)
 {
  break;
 }
 }
 return tem;
}

#include <iostream>
using namespace std;
int CommFactor2(int m, int n); //函数的声明
int main()
{
  int a, b;
  cin >> a >> b;
  cout << "这两个数的最大公约数为：" << CommFactor2(a,b)<< endl;
  return 0;
}
int CommFactor2(int m,int n)
{
  int i;
  int factor = 1;
  for (i=2;i<=m&&i<<n;i++)
  {
    while(m % i == 0 && n % i == 0)  //这里不能用if语句，因为可能会有重复的公因子
    {
      factor = factor * i;
      m = m / i;
      n = n / i;
    }
  }
  return factor;
}

#include <iostream>
using namespace std;
int CommFactor3(int m, int n); //函数的声明
int main()
{
 int a, b;
 cin >> a >> b;
 cout << "这两个数的最大公约数为：" << CommFactor2(a,b)<< endl;
 return 0;
}
int CommFactor3(int m,int n)
{
 int z = n;
 while (m % n != 0)
 {
 z = m % n;
 m = n;
 n = z;
 }
 return z;
}

#include <iostream>
using namespace std;
int CommFactor4(int m, int n); //函数的声明
int main()
{
 int a, b;
 cin >> a >> b;
 cout << "这两个数的最大公约数为：" << CommFactor4(a,b)<< endl;
 return 0;
}
int CommFactor4(int m,int n)
{
 
 while (m != n)
 {
 if (m > n)
 {
 m = m - n;
 }
 else
 {
 n = n - m;
 }
 }
 return m;
}