C++ Program to Check Abundant Number

Posted in C++ Tutorial

Updated on Oct 06, 2024

By Mari Selvan

👁️ 117 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In the realm of programming, understanding and identifying special types of numbers is a fascinating exploration. One such category is abundant numbers.

An abundant number, also known as an excessive number, is a positive integer that is smaller than the sum of its proper divisors (excluding itself).

In this tutorial, we will delve into a C++ program designed to check whether a given number is an abundant number or not.

The program will employ logic to calculate the sum of the proper divisors of a number and determine if it exceeds the number itself.

📄 Example

Let's explore the C++ code that achieves this functionality.

isAbundant.cpp

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#include <iostream>

// Function to check if a number is abundant
bool isAbundant(int num) {
  int sum = 1; // Start with 1 as every number is divisible by 1

  // Iterate from 2 to the square root of the number
  for (int i = 2; i * i <= num; ++i) {
    if (num % i == 0) {
      sum += i;
      if (i != num / i) {
        sum += num / i;
      }
    }
  }

  // If the sum of divisors exceeds the number, it is abundant
  return sum > num;
}

// Driver program
int main() {
  // Replace this value with your desired number
  int number = 12;

  // Check if the number is abundant
  if (isAbundant(number)) {
    std::cout << number << " is an abundant number." << std::endl;
  } else {
    std::cout << number << " is not an abundant number." << std::endl;
  }

  return 0;
}

💻 Testing the Program

To test the program with different numbers, simply replace the value of number in the main function.

Output

12 is an abundant number.

Compile and run the program to check if the number is an abundant number.

🧠 How the Program Works

The program defines a function isAbundant that takes a number as input and returns true if the number is abundant and false otherwise.
Inside the function, it iterates through numbers from 2 to the square root of the given number to find its divisors.
For each divisor found, it adds it to the sum, including the corresponding divisor on the other side of the square root.
Finally, it compares the sum of divisors with the original number to determine if it is abundant.

📏 Between the Given Range

Let's dive into the C++ code that checks for abundant numbers in the given range.

isAbundant.cpp

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#include <iostream>

// Function to check if a number is abundant
bool isAbundant(int num) {
  int sum = 1; // Sum of proper divisors starts with 1

  // Iterate up to the square root of num
  for (int i = 2; i * i <= num; ++i) {
    if (num % i == 0) {
      sum += i;
      if (i * i != num) {
        sum += num / i;
      }
    }
  }

  return sum > num;
}

// Driver program
int main() {
  std::cout << "Abundant numbers between 1 and 50 are: ";

  // Iterate through the range [1, 50]
  for (int i = 1; i <= 50; ++i) {
    if (isAbundant(i)) {
      std::cout << i << " ";
    }
  }

  std::cout << std::endl;

  return 0;
}

💻 Testing the Program

Output

Abundant numbers between 1 and 50 are: 12 18 20 24 30 36 40 42 48

Run the program to see the abundant numbers within the specified range.

🧠 How the Program Works

The program defines a function isAbundant that checks if a given number is abundant.
Inside the function, it iterates up to the square root of the number and calculates the sum of proper divisors.
The main function iterates through the range of numbers from 1 to 50 and prints the abundant numbers.

🧐 Understanding the Concept of Abundant Number

Before diving into the code, let's take a moment to understand abundant numbers. An abundant number is a positive integer for which the sum of its proper divisors (excluding itself) is greater than the number itself.

For example, the number 12 is abundant because its divisors (excluding 12) are 1, 2, 3, 4, 6, and the sum of these divisors is 16, which is greater than 12.

🎢 Optimizing the Program

While the provided program is effective, there are opportunities for optimization, such as caching previously calculated divisor sums to avoid redundant computations.

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