Program to Find the Given Number is Perfect Number or not in C | C Program

Here's a c program to find the given no. is perfect no. or not with output and proper explanation.

What are Perfect Numbers? A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself e.g. 6 is a perfect number - Divisors of 6 are 1, 2, 3, 6 and 1 + 2 + 3 = 6. Another perfect number is 28.

# include <stdio.h>
# include <conio.h>
void main() 
{ 
 int i, n, s = 0 ; 
 clrscr() ; 
 printf("Enter a number : ") ; 
 scanf("%d", &n) ; 
 for(i = 1 ; i < n ; i++) 
 { 
  if(n % i == 0) 
   s = s + i ; 
 } 
 if (s == n) 
  printf("\n%d is a perfect number", n) ; 
 else 
  printf("\n%d is not a perfect number", n) ; 
 getch() ; 
} 

Output of above program is 
 
Enter a number : 5
5 is not a perfect number

Enter a number : 6
6 is a perfect number

Enter a number : 28
28 is a perfect number

Explanation of above program

Here we have some integer variables let's understand the purpose of each first -

• n - This is the number that user enters.
• s - It is used to calculate the sum of all divisors of number n (excluding n itself). This sum is later compared with  the original number to check for the perfect number.
• i - This is the loop variable.

First the user enters a number to check whether that number is perfect or not. Then the for loop will run for i = 1 to i < n or up to i = n - 1. Inside the loop we check whether the number n is completely divisible by every number from 1 to n - 1 by using this expression - n % i == 0. If this expression is true then the if  condition inside the loop gets executed and inside If we add that value of i to the sum variable s. Once the loop is finished we compare the sum variable and original number i.e. n == s. If this is true that means the number n is perfect otherwise it's not a perfect number.

Lets take an example - Suppose n = 6. The for loop will execute for i = 1 to i = 5. The process is as follows -

• i = 1; Value of n % i = 6 % 1 == 0, so the if condition is executed and sum is updated as - s = s + i = 0 + 1 = 1.
• i = 2; Value of n % i = 6 % 2 == 0, so the if condition is executed and sum is updated as - s = s + i = 1 + 2 = 3.
• i = 3; Value of n % i = 6 % 3 == 0, so the if condition is executed and sum is updated as - s = s + i = 3 + 3 = 6.
• i = 4; Value of n % i = 6 % 4 == 2, The for loop will continue with the next value of i.
• i = 5; Value of n % i = 6 % 5 == 1, The for loop will terminate now.

Outside the loop n == s i.e. 6 == 6 is also true so the number 6 is perfect number.

Tip: To understand the program you can also take different values of n and try the above process yourself. It will help you to understand the process  much clearly and helps in improving your debugging ability.