# Perfect Number Program in C

## Perfect Number Program in C

In this article, you will learn how to write a Perfect Number Progam in C Programming Language. There are many methods to determine a perfect number in C, and we will go through each method and explain how it works.

## What is a Perfect Number?

A perfect number is a positive integer equal to the sum of its divisors but not the number itself.

• Example 1: The number 6 has three divisors: 1 2 3, and 1 + 2 + 3 is equal to 6. Thus, 6 is a perfect number.
• Example 2: The number 28 has five divisors: 1 2 4 7 14, and 1 + 2 + 4 + 7 + 14 is equal 28. Thus 28 is a perfect number!

## Perfect Number Program in C

Below is a program to determine if a given number is perfect or not. The idea behind the concept is to loop from 1 to the entered number, then find all the divisors for that number using the modulus operator. Then we sum up all the devisors and check if they are equal to the entered number.

#include <stdio.h>

int main ()
{
int number, sum;

printf ("Please enter a number \n");
scanf ("%d", &number);
sum = 0;
for (int i = 1; i < number; i++)
{
if (number % i == 0)
sum = sum + i;
}

if (sum == number)
{
printf ("%d is a Perfect Number", number);
}
else
{
printf ("%d is not the Perfect Number", number);
}

}

Output

Please enter a number
28
28 is a Perfect Number

## Perfect number in Program C using Recursion

Below is another way to find a perfect number in C using the recursive method.

#include <stdio.h>
int PerfectNumber (int number, int sum, int start)
{
if (number % start == 0 && start < number)
{
sum = sum + start;
}
if (start < number)
{
start++;
PerfectNumber (number, sum, start);
}
else if (start == number)
{
return sum;
}
}

int main ()
{
int number;
scanf ("%d", &number);
int i, sum = 0, start = 1;
sum = PerfectNumber (number, sum, start);
if (sum == number)
{
printf ("\n%d is Perfect Number", number);
}
else
{
printf ("\n%d is not a Perfect Number", number);
}

}

Output

Please enter a number
30

30 is not a Perfect Number

## Find All perfect Numbers Between 1 and max Number

Now, let’s say you want to find all perfect numbers between 1 and 1000. The program below will ask you for the max number, in this case, 1000, and return all perfect numbers between 1 and 1000.

Tip
There are only three Perfect Numbers between 1 and 1000! Run the program below to find out what these numbers are.

### C Program to find All perfect numbers within a given range

#include <stdio.h>

int main ()
{

int maxNumber, sum;
printf ("Please enter a max Number \n");
scanf ("%d", &maxNumber);

for (int number = 1; number <= maxNumber; number++)
{
sum = 0;

for (int i = 1; i <= number / 2; i++)
{
if (number % i == 0)
{
sum += i;
}
}

if (sum == number)
{
printf ("%d is a Perfect Number\n", number);
}
}

return 0;
}

Output

Please enter a max Number
1000
6 is a Perfect Number
28 is a Perfect Number
496 is a Perfect Number