The largest integer which can perfectly divide two integers is known as GCD or HCF of those two numbers.

Example 1: Find GCD using while loop

#include <iostream>
using namespace std;

int main(){
    int n1, n2;

    cout << "Enter two numbers: ";
    cin >> n1 >> n2;
    
    while(n1 != n2)
    {
        if(n1 > n2)
            n1 -= n2;
        else
            n2 -= n1;
    }

    cout << "HCF = " << n1;
    return 0;
}

Output

Enter two numbers: 78
52
HCF = 26

In above program, smaller number is subtracted from larger number and that number is stored in place of larger number.

This process is continued until, two numbers become equal which will be HCF.

Example: 2. Find HCF/GCD using for loop

#include <iostream>
using namespace std;

int main(){
    int n1, n2, hcf;
    cout << "Enter two numbers: ";
    cin >> n1 >> n2;

    // Swapping variables n1 and n2 if n2 is greater than n1.
    if ( n2 > n1) {   
        int temp = n2;
        n2 = n1;
        n1 = temp;
    }
    
    for (int i = 1; i <=  n2; ++i) {
        if (n1 % i == 0 && n2 % i ==0) {
            hcf = i;
        }
    }

    cout << "HCF = " << hcf;
    return 0;
}

The logic of this program is simple.

In this program, small integer between n1 and n2 is stored in n2. Then the loop is iterated from i = 1 to i <= n2 and in each iteration, value of i is increased by 1.

If both numbers are divisible by i then, that number is stored in variable hcf.

When the iteration is finished, HCF will be stored in variable hcf.