C++ Program to Check Amicable Number

Posted in C++ Tutorial

Updated on Oct 06, 2024

By Mari Selvan

👁️ 45 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In the realm of programming, exploring number properties is a fascinating journey. One interesting concept is that of amicable numbers.

Amicable numbers are two numbers that share a unique relationship: the sum of the proper divisors of each number is equal to the other number.

In simpler terms, the sum of the divisors of one number is the other number itself.

In this tutorial, we'll explore a C++ program designed to check whether two given numbers are amicable or not.

The program will identify and compare the sum of proper divisors to determine if the numbers form an amicable pair.

📄 Example

Let's take a look at the C++ code that accomplishes this task.

areAmicable.cpp

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#include <iostream>

// Function to calculate the sum of proper divisors of a number
int sumOfDivisors(int num) {
  int sum = 1; // Start with 1 as every number is divisible by 1

  for (int i = 2; i * i <= num; ++i) {
    if (num % i == 0) {
      sum += i;
      if (i != num / i) {
        sum += num / i;
      }
    }
  }

  return sum;
}

// Function to check if two numbers are amicable
bool areAmicable(int num1, int num2) {
  return sumOfDivisors(num1) == num2 && sumOfDivisors(num2) == num1;
}

// Driver program
int main() {
  // Replace these values with your desired numbers
  int number1 = 220;
  int number2 = 284;

  // Check if the numbers are amicable
  if (areAmicable(number1, number2)) {
    std::cout << number1 << " and " << number2 << " are amicable numbers." << std::endl;
  } else {
    std::cout << number1 << " and " << number2 << " are not amicable numbers." << std::endl;
  }

  return 0;
}

💻 Testing the Program

To test the program with different numbers, replace the values of number1 and number2 in the main function.

Output

220 and 284 are amicable numbers.

Compile and run the program to check if the numbers form an amicable pair.

🧠 How the Program Works

The program defines a function sumOfDivisors to calculate the sum of proper divisors for a given number.
Another function, areAmicable, checks whether two numbers are amicable by comparing the sums of their proper divisors.
The main function tests the amicability of two numbers and prints the result.

🧐 Understanding the Concept of Amicable Numbers

Amicable numbers exhibit a unique relationship where the sum of the proper divisors of each number is equal to the other number.

For example, the pair (220, 284) is amicable because the sum of divisors of 220 is 284, and the sum of divisors of 284 is 220.

🎢 Optimizing the Program

While the provided program is effective, you may explore optimizations such as caching the results of the sum of divisors to enhance performance for repeated calculations.

Feel free to incorporate and modify this code as needed for your specific use case. Happy coding!