Reduce the fraction to its lowest form

Given two integers x and y and where x is divisible by y. It can be represented in the form of a fraction x/y. The task is to reduce the fraction to its lowest form.
Examples:

Input : x = 16, y = 10
Output : x = 8, y = 5

Input : x = 10, y = 8
Output : x = 5, y = 4

Approach: Both of the values x and y will be divisible by their greatest common divisor. So if we divide x and y from the gcd(x, y) then x and y can be reduced to its simplest form.

Algorithm:

• Create the “reduceFraction” function, which has the two integer inputs x and y.
• Declare the variable d as an integer.
• Call the __gcd() method with the inputs x and y, and then save the outcome in d.
• Divide x by d, then put the outcome back into x.
• Divide y by d, then add the answer back into y.
• Print the lowered fraction together with the revised x and y values.
  

Below is the implementation of the above approach: 

C++

// C++ program to reduce a fraction x/y
// to its lowest form

#include <bits/stdc++.h>
using namespace std;

// Function to reduce a fraction to its lowest form
void reduceFraction(int x, int y)
{
    int d;
    d = __gcd(x, y);

    x = x / d;
    y = y / d;

    cout << "x = " << x << ", y = " << y << endl;
}

// Driver Code
int main()
{
    int x = 16;
    int y = 10;

    reduceFraction(x, y);

    return 0;
}

Java

// Java program to reduce a fraction x/y
// to its lowest form
class GFG
{

// Function to reduce a fraction to its lowest form
static void reduceFraction(int x, int y)
{
    int d;
    d = __gcd(x, y);

    x = x / d;
    y = y / d;

    System.out.println("x = " + x + ", y = " + y);
}

static int __gcd(int a, int b)
{
    if (b == 0)
        return a;
    return __gcd(b, a % b);

}

// Driver Code
public static void main(String[] args)
{
    int x = 16;
    int y = 10;

    reduceFraction(x, y);
}
}

/* This code contributed by PrinciRaj1992 */

Python3

# Python3 program to reduce a fraction x/y
# to its lowest form
from math import gcd

# Function to reduce a fraction
# to its lowest form
def reduceFraction(x, y) :

    d = gcd(x, y);

    x = x // d;
    y = y // d;

    print("x =", x, ", y =", y);

# Driver Code
if __name__ == "__main__" :

    x = 16;
    y = 10;

    reduceFraction(x, y);

# This code is contributed by Ryuga

C#

// C# program to reduce a fraction x/y
// to its lowest form
using System;

class GFG
{

// Function to reduce a fraction to its lowest form
static void reduceFraction(int x, int y)
{
    int d;
    d = __gcd(x, y);

    x = x / d;
    y = y / d;

    Console.WriteLine("x = " + x + ", y = " + y);
}

static int __gcd(int a, int b)
{
    if (b == 0)
        return a;
    return __gcd(b, a % b);

}

// Driver Code
public static void Main(String[] args)
{
    int x = 16;
    int y = 10;

    reduceFraction(x, y);
}
}

// This code has been contributed by 29AjayKumar

PHP

<?php
// PHP program to reduce a fraction x/y
// to its lowest form

// Function to reduce a fraction to its lowest form
function reduceFraction($x, $y)
{
    $d;
    $d = __gcd($x, $y);

    $x = $x / $d;
    $y = $y / $d;

    echo("x = " . $x . ", y = " . $y);
}

function __gcd($a, $b)
{
    if ($b == 0)
        return $a;
    return __gcd($b, $a % $b);

}

// Driver Code
$x = 16;
$y = 10;

reduceFraction($x, $y);

// This code is contributed by Rajput-Ji
?>

Javascript

<script>

// Javascript program to reduce a fraction x/y
// to its lowest form

// Function to reduce a fraction to its lowest form
function reduceFraction(x, y)
{
    let d;
    d = __gcd(x, y);

    x = parseInt(x / d);
    y = parseInt(y / d);

    document.write("x = " + x + ", y = " + y);
}

function __gcd(a, b)
{
    if (b == 0)
        return a;
    return __gcd(b, a % b);

}

// Driver Code
    let x = 16;
    let y = 10;

    reduceFraction(x, y);

</script>

Output

x = 8, y = 5

Time Complexity: O(log(max(x,y)))
Auxiliary Space: O(log(max(x,y)))