C++ Program to Check Perfect Number

Posted in C++ Tutorial

Updated on Oct 06, 2024

By Mari Selvan

👁️ 92 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In the realm of programming, exploring the properties of numbers is a fascinating task. One such special type of number is a perfect number.

A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself).

In this tutorial, we will explore a C++ program designed to check whether a given number is a perfect number.

The program involves finding the sum of the proper divisors of the number and checking if it equals the original number.

📄 Example

Let's delve into the C++ code that accomplishes this task.

isPerfectNumber.cpp

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#include <iostream>

// Function to check if a number is a perfect number
bool isPerfectNumber(int number) {
  int sum = 0;

  // Iterate through potential divisors up to half of the number
  for (int i = 1; i <= number / 2; ++i) {
    if (number % i == 0) {
      sum += i; // Add the divisor to the sum
    }
  }

  // If the sum of divisors equals the number, it is a perfect number
  return sum == number;
}

// Driver program
int main() {
  // Replace this value with the number you want to check
  int number = 28;

  // Call the function to check if the number is a perfect number
  if (isPerfectNumber(number))
    std::cout << number << " is a perfect number." << std::endl;
  else
    std::cout << number << " is not a perfect number." << std::endl;

  return 0;
}

💻 Testing the Program

To test the program with different numbers, modify the value of number in the main program.

Output

28 is a perfect number.

Compile and run the program to check if the specified number is a perfect number.

🧠 How the Program Works

The program defines a function isPerfectNumber that takes an integer number as input and returns true if the number is a perfect number, and false otherwise.
The function iterates through potential divisors up to half of the number, adding the divisors to the sum.
Inside the main program, replace the value of number with the desired number you want to check.
The program calls the isPerfectNumber function and prints the result.

📏 Between the Given Range

Let's delve into the C++ code that identifies perfect numbers in the specified range.

isPerfect.cpp

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#include <iostream>

// Function to check if a number is perfect
bool isPerfect(int num) {
  int sum = 1; // 1 is always a divisor

  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 << "Perfect Numbers in the range 1 to 50:\n";

  for (int i = 1; i <= 50; ++i) {
    if (isPerfect(i)) {
      std::cout << i << " ";
    }
  }

  std::cout << std::endl;

  return 0;
}

💻 Testing the Program

Output

Perfect Numbers in the range 1 to 50:
6 28

Compile and run the program to see the perfect numbers in the specified range.

🧠 How the Program Works

The program defines a function isPerfect that checks if a given number is a perfect number.
Inside the function, it iterates through potential divisors and calculates the sum of divisors.
The main function tests each number in the range from 1 to 50 using the isPerfect function and prints the perfect numbers.

🧐 Understanding the Concept of Perfect Number

Before delving into the code, let's understand the concept of perfect numbers. A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself).