Find Sum of Odd Factors of a Number in C++

Given with a positive integer and the task is to generate the odd factors of a number and finding out the sum of given odd factors.

Example

Input-: number = 20
Output-: sum of odd factors is: 6
Input-: number = 18
Output-: sum of odd factors is: 13

So, result = 1 + 5 = 6

Approach used in the below program is as follows −

• Input the number for calculating the sum of odd factors of that number
• Ignore the digit 0 and 2 because both are even digits and store the digit 1 because it is an odd digit
• Start the loop from 3 till square root of a number
• Traverse till number % i is returning 0 and keep dividing the number with the value of i
• In the loop keep setting the value of temporary variable to temp = temp * i
• Set the total to total + temp
• Return the value of final res variable and print the result

Algorithm

START
Step 1-> Declare function to calculate sum of odd factors
   int sum(int num)
   declare int res = 1
   Loop While(num % 2 == 0)
      set num = num / 2
   End
   Loop For int i = 3 and i <= sqrt(num) and i++
      declare int count = 0 and total = 1
      declare int temp = 1
      Loop while (num % i == 0)
         count++
         set num = num / i
         set temp *= i
         set total += temp
      End
      set res = res*total
   End
   IF (num >= 2)
      set res *= (1 + num)
   End
   return res
Step 2-> In main()
   Declare int num = 20
   call sum(num)
STOP

Example

#include <bits/stdc++.h>
using namespace std;
//calculate sum of odd factors
int sum(int num) {
   int res = 1;
   while (num % 2 == 0)
   num = num / 2;
   for (int i = 3; i <= sqrt(num); i++) {
      int count = 0, total = 1 ;
      int temp = 1;
      while (num % i == 0) {
         count++;
         num = num / i;
         temp *= i;
         total += temp;
      }
      res = res*total;
   }
   if (num >= 2)
   res *= (1 + num);
   return res;
}
int main() {
   int num = 20;
   cout<<"sum of odd factors is : ";
   cout <<sum(num);
   return 0;
}

Output

sum of odd factors is : 6