C++ Program to check whether two numbers are Friendly Pair(Amicable number) or not

July 29, 2019

Program to check whether two numbers are Friendly Pair(Amicable number) or not

Here we will discuss how to check whether a pair of numbers is a Friendly Pair(Amicable numbers) or not using C++ programming language.

Amicable numbers are two different numbers related in a way such that the sum of the proper divisors of each is equal to the other number. A proper divisor is a positive factor of that number other than the number itself ,for Example proper divisors of 6 are 1, 2, and 3.

The smallest pair of amicable numbers is (220, 284). They are amicable because the sum of proper divisors of 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110) is 284; and the sum of proper divisors of 284 (1, 2, 4, 71 and 142) is 220.

Program to check for Amicable numbers

Working

Let’s see how the code works:

  • User gives two inputs(numbers to check).
  • Inputs are stored in int type variables say first & second.
  • A function findAmicable() is called with first and second as parameters.
    • Divisors of first are found, added and stored in an int type variable say sum1.
    • Divisors of second are found, added and stored in another variable sum2.
    • If first is equal to sum2 and second is equal to sum1 then they are Amicable numbers
    • Otherwise they are not Amicable numbers

C++ Code

//C++ Program
//Friendly Pair(Amicable number) or not
#include<iostream>
using namespace std;
// function to check Friendly pairs
void findAmicable(int first, int second)
{
	int sum1=0,sum2=0;
	for(int i=1; i<=first/2 ; i++)
	{
		//finding and adding divisors of first number
		if(first%i==0)
			sum1=sum1+i;
	}
	for(int i=1; i<=second/2 ; i++)
	{
		//finding and adding divisors of second number
		if(second%i==0)
			sum2=sum2+i;
	}
	//ckecking for friendly pair
	if(first==sum2 && second==sum1)
		cout<<"Fiendly Pair("<<first<<","<<second<<")";
	else
		cout<<"Not a Fiendly Pair";
}
//main program
int main()
{
	int first,second;
	cout<<"Enter first number : ";
	//user input
	cin>>first;
	cout<<"Enter second number : ";
	//user input
	cin>>second;
	//calling function
	findAmicable(first,second);
	return 0;
}

Output

Enter first number : 220
Enter second number : 284
Fiendly Pair(220,284)

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