C Program to Check for Perfect Numbers

A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself. Proper divisors of a number are the positive divisors other than the number itself. For example, 28 is a perfect number because its proper divisors are 1, 2, 4, 7, and 14, and their sum is 1 + 2 + 4 + 7 + 14 = 28.

In this article, we will write a C program to check whether a given number is a perfect number or not. We will start by understanding the concept of perfect numbers, then outline the algorithm, and finally provide the complete C program with detailed explanations.

Understanding Perfect Numbers

A perfect number is a number that satisfies the following condition:

Sum of proper divisors=Number

For example:

• 6 is a perfect number because its proper divisors are 1, 2, and 3, and their sum is 1 + 2 + 3 = 6.
• 28 is a perfect number because its proper divisors are 1, 2, 4, 7, and 14, and their sum is 1 + 2 + 4 + 7 + 14 = 28.

Algorithm to Check for a Perfect Number

1. Input the number: Get the number from the user.
2. Find proper divisors: Iterate through all numbers from 1 to the given number - 1 and find the divisors.
3. Sum the divisors: Calculate the sum of all proper divisors.
4. Compare the sum with the original number: If the sum is equal to the original number, it is a perfect number; otherwise, it is not.

Write a C Program to Check for Perfect Numbers

Here is the complete C program to check whether a given number is a perfect number or not:

#include <stdio.h>

int main() {
    int num, sum = 0;

    // Input the number from the user
    printf("Enter an integer: ");
    scanf("%d", &num);

    // Find and sum all proper divisors of the number
    for (int i = 1; i <= num / 2; i++) {
        if (num % i == 0) {
            sum += i;
        }
    }

    // Check if the sum of divisors is equal to the original number
    if (sum == num && num != 0) {
        printf("%d is a perfect number.", num);
    } else {
        printf("%d is not a perfect number.", num);
    }

    return 0;
}

Output

Enter an integer: 496
496 is a perfect number.

Explanation of the Code

1. Input the Number:
   • scanf("%d", &num); reads the integer input from the user.
2. Find and Sum Proper Divisors:
   • The for loop iterates through all numbers from 1 to num / 2 to find the divisors.
   • if (num % i == 0) checks if i is a divisor of num.
   • sum += i; adds the divisor to the sum.
3. Check for Perfect Number:
   • The condition if (sum == num && num != 0) checks if the sum of the proper divisors is equal to the original number. If true, it prints that the number is a perfect number; otherwise, it states that it is not.

Example Runs

Let's look at some example runs to see how the program works:

Example 1

Enter an integer: 6
6 is a perfect number.

• Calculation: Proper divisors are 1, 2, 3. Sum = 1 + 2 + 3 = 6.

Example 2

Enter an integer: 28
28 is a perfect number.

• Calculation: Proper divisors are 1, 2, 4, 7, 14. Sum = 1 + 2 + 4 + 7 + 14 = 28.

Example 3

Enter an integer: 12
12 is not a perfect number.

• Calculation: Proper divisors are 1, 2, 3, 4, 6. Sum = 1 + 2 + 3 + 4 + 6 = 16.