Perfect Number Between 1 and Given Input

In mathematics, a perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). This code finds and displays all perfect numbers within the specified range.

#include<stdio.h>
#include<math.h>
main()
{
  int num,i,sum,j;
  printf("Enter a number to know all perfect numbers till n\n");
  scanf("%d",&num);
  printf("The perfect numbers between 1 and %d are:",num);
  for(i=1;i<=num;i++)
  {
    sum=0;
    for(j=1;j<i;j++)
    {
      if(i%j==0)
      {
        sum+=j;
      }
    }
    if(sum==i)
    {
      printf("%d\n",i);
    }
  }
}

Enter a number to know all perfect numbers till n
9654
The perfect numbers between 1 and 9654 are:6
28
496
8128

Explanation:

Here’s a step-by-step explanation of the code:

Header File:

• The program includes the standard C library header <stdio.h> for input and output operations and <math.h> for mathematical operations.

Main Function:

• The main function is the entry point of the program.

Variable Declarations:

• int num, i, sum, j; Declares integer variables for storing user input, looping variables, and the sum of divisors.

Input for a Number:

• The user is prompted to enter a number using scanf, and the value is stored in the variable num.

Output Prompt:

• The code displays a message informing the user that it will find perfect numbers up to the value of num.

Finding Perfect Numbers:

• The code enters a for loop that iterates from 1 to num.
• For each number i in this range, it initializes the sum variable to 0.
• It then enters another for loop with variable j starting from 1 and iterating up to i-1.
• Within the inner loop, it checks if i is divisible by j (i.e., i % j == 0).
• If it is divisible, it adds j to the sum.
• After the inner loop finishes, it checks if the sum is equal to i. If it is, then i is a perfect number.
• If i is a perfect number, it is displayed using printf.

Output:

• The code lists all the perfect numbers found within the range from 1 to the user-provided number num.