Find sum of odd factors of a number using C++.

In this section, we will see how we can get the sum of all odd prime factors of a number in an efficient way. There is a number say n = 1092, we have to get all factors of this. The prime factors of 1092 are 2, 2, 3, 7, 13. The sum of all odd factors is 3+7+13 = 23. To solve this problem, we have to follow this rule −

• When the number is divisible by 2, ignore that factor, and divide the number by 2 repeatedly.
• Now the number must be odd. Now starting from 3 to square root of the number, if the number is divisible by current value, then add the factor with the sum, and change the number by divide it with the current number then continue.
• Finally, the remaining number will also be added if the remaining number is odd

Let us see the algorithm to get a better idea.

Algorithm

printPrimeFactors(n):
begin
sum := 0
   while n is divisible by 2, do
      n := n / 2
   done
   for i := 3 to , increase i by 2, do
      while n is divisible by i, do
         sum := sum + i
         n := n / i
      done
   done
   if n > 2, then
      if n is odd, then
         sum := sum + n
      end if
   end if
end

Example

#include<iostream>
#include<cmath>
using namespace std;
int sumOddFactors(int n){
   int i, sum = 0;
   while(n % 2 == 0){
      n = n/2; //reduce n by dividing this by 2
   }
   //as the number is not divisible by 2 anymore, all factors are odd
   for(i = 3; i <= sqrt(n); i=i+2){ //i will increase by 2, to get only odd numbers
      while(n % i == 0){
         sum += i;
         n = n/i;
      }
   }
   if(n > 2){
      if(n%2 == 1)
      sum += n;
   }
   return sum;
}
main() {
   int n;
   cout << "Enter a number: ";
   cin >> n;
   cout <<"Sum of all odd prime factors: "<< sumOddFactors(n);
}

Output

Enter a number: 1092
Sum of all odd prime factors: 23