C++ Program for Common Divisors of Two Numbers

The common divisor of two numbers are the numbers that are divisors of both of them.

For example,

The divisors of 12 are 1, 2, 3, 4, 6, 12.

The divisors of 18are 1, 2, 3, 6, 9, 18.

Thus, the common divisors of 12 and 18 are 1, 2, 3, 6.

The greatest among these is, perhaps unsurprisingly, called the greatest common divisor of 12 and 18. The usual mathematical notation for the greatest common divisor of two integers a and b are denoted by (a, b). Hence, (12, 18) = 6.

The greatest common divisor is important for many reasons. For example, it can be used to calculate the LCM of two numbers, i.e., the smallest positive integer that is a multiple of these numbers. The least common multiple of the numbers a and b can be calculated as ab(a, b).

For example, the least common multiple of 12 and 18 is 12·18(12, 18) =12 · 18.6

Input: a = 10, b = 20
Output: 1 2 5 10
// all common divisors are 1 2 5 10

Explanation 

Integers that can exactly divide both numbers (without a remainder).

Example

#include <iostream>
using namespace std;
int main() {
   int n1, n2, i;
   n1=10;
   n2=20;
   for(i=1; i <= n1 && i <= n2; ++i) {
      if(n1%i==0 && n2%i==0) {
         cout<<i<<"\t";
      }
   }
}