Question

{
/* Write a program in C++ to find the perfect numbers between 1 and 500.
The perfect numbers between 1 to 500 are:
6
28
496*/
   int sum = 0;
   int i = 1;
   int j = 1;
   for (i ; i <= 100; i++)
   {
       for (j; j <= 100; j++)
       {
           if (j < i)//Line 55
           {
              
           if (i % j == 0)
               sum = sum + j;
           }
          
       }

       if (sum == i)
      
           cout << i << " ";
       j = 1;//line 66
       sum = 0;
      
   }
  
   return 0;
}

Can someone please explain the code above and how it works. what is the purpose of the comparison on line 55 and I on line 66?

Answer 1

#include<iostream>

using namespace std;

int main()
{
   int sum = 0;
   int i = 1;
   int j = 1;

   //perfect number is equal to sum of its divisors
   //Example : number 6
   //divisors of 6 are : 1,2,3 = sum of these values is 1+2+3 = 6
   //below code is implement by using above logic
   //Here i is the number to check,if it is perfect number or not
   for (i ; i <= 500; i++)
   {
       //here j is used to divide i value
       for (j; j < i; j++)
       {
           //This condition used to check the value j is less than i
           //We have to find the divisor of i upto i-1 value.So we have to wrote the condition (j<i)
          //For example i value is 6
          //To check is perfect number or not.we have to divide i value with j value and it gives reminder zero and also some of those j values should equal to i value
         //suppose i = 6
         //6%1 = reminder 0
         //6%2 = reminder 0
         //6%3 = reminder 0
         //6%4 = remimder 2
         //6%5 = remimder 1.After this the condition will fail.
           if (j < i)//Line 55
           {
               //This condition is used to find the number i is divisible by j are not.Then it add the j value with sum.
               //In above example,sum the value of j which got the reminder 0.
               //1+2+3 = 6.So 6 is the perfect number
               if (i % j == 0)
                 sum = sum + j;
           }
       }
       //if sum equal to i
       //At i = 6,sum will become 6.Then it prints the sum
       if (sum == i)
          cout << i << " ";
       //we have to divide every number (i)starting from 1 to i-1.But after completion of inner for loop, j value will different not equal to 1.So we have to initialize j value with 1 before going to outer for loop.So here it writtern as j = 1.Otherwise from next iteration,i will not divide from 1.
       j = 1;//line 66
       sum = 0;
     }
     return 0;
}