Perfect Numbers Program in C

Problem

Problem Statement:

Write a program to check whether a given number is a perfect number.

Example 1:

Input: 
6

Output:  
6 is a perfect number.

Explanation:
A perfect number is a positive integer which is equal to the sum of its positive divisors, excluding itself. 

The positive divisors of 6 are 1, 2 and 3. 
Sum = 1 + 2 + 3 = 6.

Hence, 6 is a perfect number.

Example 2:

Input: 
12

Output:  
12 is not a perfect number. 

Example 3:

Input:
1

Output:
1 is not a perfect number. 

Explanation:
1 is not a perfect number because the only divisor of 1 is 1 itself. According to the definition, a perfect number is a positive integer which is equal to the sum of its positive divisors, excluding itself. So, clearly 1 is not a perfect number.

Expectations:

You need to write the complete program using the following template as the starter:

#include <stdio.h>

int main() {
    int n;
    
    printf("Enter a number: ");
    scanf("%d", &n);
    
    // Write your code here
    
    return 0;
}

Copy and paste the above code in your favorite IDE and start writing your code after the comment “// Write your code here.”

Sample Test Cases:

To verify the program you have written, go ahead and test your program using the following test cases:

Don’t forget to try the code on your own before diving into the solution.

Solution

We can use either for loop or while loop to solve this problem.

Approach 1 – Using for Loop

// Program to check whether a given number is a perfect number using for loop.
#include <stdio.h>

int main() {
    int n;
    
    printf("Enter a number: ");
    scanf("%d", &n);
    
    // Write your code here
    
    int sum = 0;
    // Iterate from 1 through half of the number
    for(int i = 1; i <= n/2; i++) {
        // if divisor is found, then add it to the previous sum
        if (n % i == 0) {
            sum += i;
        }
    }
    
    if (sum == n)
        printf("%d is a perfect number.", n);
    else
        printf("%d is not a perfect number.", n);    
    
    return 0;
}

In the above program:

• User is asked for a number. 
• The loop runs from 1 to the half of the number (because numbers after the first half of the number can never be proper divisors of the number). 
• Inside the loop
  • If the current number is divisible by the given number, then the divisor is found, and it is added to the sum. 
  • The loop will continue and check for other numbers.
• Outside the loop
  • If the sum obtained is equal to the given number, then we know that the given number is a perfect number.
  • Otherwise it is not. 

Approach 2 – Using while Loop

// Program to check whether a given number is a perfect number using while loop.
#include <stdio.h>

int main() {
    int n;
    
    printf("Enter a number: ");
    scanf("%d", &n);
    
    // Write your code here
    
    int sum = 0, i = 1;
    // Iterate from 1 through half of the number
    while(i <= n/2) {
        // if divisor is found, then add it to the previous sum
        if (n % i == 0) {
            sum += i;
        }
        i++;
    }
    
    if (sum == n)
        printf("%d is a perfect number.", n);
    else
        printf("%d is not a perfect number.", n);    
    
    return 0;
}

In the above program, the for loop is replaced by the while loop. This does not affect the logic of the program. The logic is the same.