An integer is said to be a perfect number if the sum of its divisors, including

Question

An integer is said to be a perfect number if the sum of its divisors, including 1 (but not the number itself), is equal to the number. For example, 6 is a perfect number because 1+2+3=6. Write a function PERFECT that determines whether a number is a perfect number. The function should have an integer as its only parameter and return the boolean value true if the number is perfect, false otherwise. Write a program that uses a for loop and calls this function to determine and display all the perfect numbers between 1 and 100.


Hint: include diagnostic statements in the function to display the divisors of each perfect number to confirm that the number is indeed perfect.

Explanation / Answer

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#include<iostream>
using namespace std;
bool PERFECT(int);
int main()
{int num;
cout<<"The perfect numbers between 1 and 100 are: ";
for(num=1;num<=100;num++)
{if(PERFECT(num))
    cout<<num<<endl;
}

system("pause");
return 0;
}
bool PERFECT(int num)
{int sum,i,count=0;
count=0;
sum=0;
for(i=1;i<num;i++)
    if(num%i==0)
        {sum+=i;
        count++;
        }
if(sum==num)
     {
       for(i=1;i<num;i++)
            if(num%i==0)
                 {count--;
                  cout<<i;
                  if(count>0)
                      cout<<" + ";
                      }
          cout<<" = ";
          return true;
         
          }
return false;
}

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