# Program to balance the given Chemical Equation

Given the values x, y, p, q of a simple chemical equation of the type: The task is to find the values of constants b1, b2, b3 such that the equation is balanced on both sides and it must be the reduced form.

Examples:

Input: x = 2, y = 3, p = 4, q = 5
Output: b1 = 6, b2 = 5, b3 = 3

Input: x = 1, y = 2, p = 3, q = 1
Output: b1 = 3, b2 = 2, b3 = 1

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. Check if p % x = 0 and q % y = 0 or not.
2. If yes, then simply we can say that
b1 = p / x,
b2 = q / y, and
b3 = 1
3. Else we need to use gcd to compute b1, b2, b3. We need the reduced form so gcd can help with it.

Below is the implementation of the above approach.

## C++

 // C++ program to balance  // the given Chemical Equation  #include  using namespace std;     // Function to calculate GCD  int gcd(int a, int b)  {      if (b == 0)          return a;      return gcd(b, a % b);  }     // Function to calculate b1, b2 and b3  void balance(int x, int y, int p, int q)  {      // Variable declaration      int b1, b2, b3;         if (p % x == 0 && q % y == 0) {          b1 = p / x;          b2 = q / y;          b3 = 1;      }         else {          p = p * y;          q = q * x;          b3 = x * y;             // temp variable to store gcd          int temp = gcd(p, gcd(q, b3));             // Computing GCD          b1 = p / temp;          b2 = q / temp;          b3 = b3 / temp;      }         cout << b1 << " " << b2           << " " << b3 << endl;  }     // Driver code  int main()  {      int x = 2, y = 3, p = 4, q = 5;         balance(x, y, p, q);  }

## Java

 // Java program to balance  // the given Chemical Equation     import java.util.*;     class GFG{      // Function to calculate GCD  static int gcd(int a, int b)  {      if (b == 0)          return a;      return gcd(b, a % b);  }      // Function to calculate b1, b2 and b3  static void balance(int x, int y, int p, int q)  {      // Variable declaration      int b1, b2, b3;          if (p % x == 0 && q % y == 0) {          b1 = p / x;          b2 = q / y;          b3 = 1;      }          else {          p = p * y;          q = q * x;          b3 = x * y;              // temp variable to store gcd          int temp = gcd(p, gcd(q, b3));              // Computing GCD          b1 = p / temp;          b2 = q / temp;          b3 = b3 / temp;      }          System.out.print(b1 + " " +  b2          + " " +  b3 +"\n");  }      // Driver code  public static void main(String[] args)  {      int x = 2, y = 3, p = 4, q = 5;          balance(x, y, p, q);  }  }     // This code contributed by Rajput-Ji

## Python3

 # Python 3 program to balance  # the given Chemical Equation     # Function to calculate GCD  def gcd(a,b):      if (b == 0):          return a      return gcd(b, a % b)     # Function to calculate b1, b2 and b3  def balance(x, y, p, q):         # Variable declaration      if (p % x == 0 and q % y == 0):          b1 = p // x          b2 = q // y          b3 = 1        else:          p = p * y          q = q * x          b3 = x * y             # temp variable to store gcd          temp = gcd(p, gcd(q, b3))             # Computing GCD          b1 = p // temp          b2 = q // temp          b3 = b3 // temp         print(b1,b2,b3)     # Driver code  if __name__ == '__main__':      x = 2     y = 3     p = 4     q = 5        balance(x, y, p, q)     # This code is contributed by Surendra_Gangwar

## C#

 // C# program to balance  // the given Chemical Equation     using System;     public class GFG{     // Function to calculate GCD  static int gcd(int a, int b)  {      if (b == 0)          return a;      return gcd(b, a % b);  }     // Function to calculate b1, b2 and b3  static void balance(int x, int y, int p, int q)  {      // Variable declaration      int b1, b2, b3;         if (p % x == 0 && q % y == 0) {          b1 = p / x;          b2 = q / y;          b3 = 1;      }         else {          p = p * y;          q = q * x;          b3 = x * y;             // temp variable to store gcd          int temp = gcd(p, gcd(q, b3));             // Computing GCD          b1 = p / temp;          b2 = q / temp;          b3 = b3 / temp;      }         Console.Write(b1 + " " + b2                    + " " + b3 +"\n");  }     // Driver code  public static void Main(String[] args)  {      int x = 2, y = 3, p = 4, q = 5;         balance(x, y, p, q);  }  }     // This code is contributed by Rajput-Ji

Output:

6 5 3


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