Solution:

### What is a Perfect Number?

In number theory, a perfect number may be defined as 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.

So we will find all positive divisors(excluding the number itself) of the given number and get sum of these. If the sum is equal to the given number then IT IS A PERFECT NUMBER, otherwise not. For example, 6 is a perfect number. Because, sum of proper divisors of 6 is:

1+2+3 = 6.

### Here is the C++ Program Code for PERFECT NUMBER CHECK!

/*

Write a C++ Program to input a positive number, then check

whether this number is a perfect number?

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Visit Www.ForFreeEducation.Blogspot.Com

*/

#include<iostream.h>

#include<conio.h>

void main()

{

clrscr();

long number, sum=0, counter, mid, count=0;

cout<<"\n Enter the positive number\nto check for Perfect Number= ";

cin>>number;

mid = number / 2;

cout<<"\n\n ----------- Results ------------";

cout<<"\n\n Proper Positive Divisors of \n that is divisors excluding \nthe number itself "<<number<<" are=";

for (counter = 1; counter <= mid; counter++)

{

cout<<"\n \t"<<counter;

sum = sum + counter;

}

cout<<"\n Sum of Proper divisors ="<<sum;

if ( number == sum )

cout<<"\n The number is Perfect Number";

else

cout<<"\n the number is not a Perfect Number";

getch();

}