Reduce the fraction to its lowest form in C++

Given two integers Num1 and Num2 as input. The integers can be represented as fraction Num1/Num2. The goal is to reduce this fraction to its lowest form.

Using GCD to find highest denominator

• We will calculate the greatest common divisor of both numbers.

• Divide both numbers by that gcd

• Set both variables as quotient after division.

• Lowest fraction will be Num1/Num2.

Examples

Input − Num1=22 Num2=10

Output − Num1 = 11 Num2 = 5

Lowest Fraction : 11/5

Explanation− GCD of 22 and 10 is 2.

22/2=11 and 10/2=5

Lowest fraction is 11/5

Input− Num1=36 Num2=40

Output− Num1 = 9 Num2 = 10

Lowest Fraction : 9/10

Explanation − GCD of 36 and 40 is 4.

40/4=10 and 36/4=9

Lowest fraction is 9/10

Approach used in the below program is as follows

In this approach we will first calculate the GCD of input numbers using a recursive approach. Divide both numbers by GCD and obtain quotients. These quotients will be part of the lowest fraction.

• Take the input variables Num1 and Num2.

• Function findGCD(int a, int b) takes num1 and num2 and returns the gcd of both.

• If b is 0 return a else return findGCD(b,a%b).

• Function lowestFraction(int num1, int num2) takes both numbers as input and prints the lowest fraction.

• Take variable denom for gcd.

• Set num1=num1/denom and num2=num2/denom.

• Print num1 and num2.

• Print the lowest fraction as num1/num2.

Example

#include <bits/stdc++.h>
using namespace std;
int findGCD(int a, int b) {
   if (b == 0)
      return a;
      return findGCD(b, a % b);
   }
   void lowestFraction(int num1, int num2){
      int denom;
      denom = findGCD(num1,num2);
      num1/=denom;
      num2/=denom;
      cout<< "Num1 = " << num1<<endl;
      cout<< "Num2 = " << num2<<endl;
      cout<< "Lowest Fraction : "<<num1<<"/"<<num2;
}
int main(){
   int Num1 = 14;
   int Num2 = 8;
   lowestFraction(Num1,Num2);
   return 0;
}

Output

If we run the above code it will generate the following Output

Num1 = 7
Num2 = 4
Lowest Fraction : 7/4