HCF of array of fractions (or rational numbers)

Given a fraction series. Find the H.C.F of a given fraction series.
Examples:

Input : [{2, 5}, {8, 9}, {16, 81}, {10, 27}]
Output :  2, 405 
Explanation : 2/405 is the largest number that
divides all 2/5, 8/9, 16/81 and 10/27.

Input : [{9, 10}, {12, 25}, {18, 35}, {21, 40}]
Output : 3, 1400

Approach:

Find the H.C.F of numerators.
Find the L.C.M of denominators.
Calculate fraction of H.C.F/L.C.M.
Reduce the fraction to Lowest Fraction.

C++

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// CPP program to find HCF of array of 
// rational numbers (fractions).
#include <iostream>
using namespace std;
  
// hcf of two number
int gcd(int a, int b)
{
    if (a % b == 0)
        return b;
    else
        return (gcd(b, a % b));
}
  
// find hcf of numerator series
int findHcf(int** arr, int size)
{
    int ans = arr[0][0];    
    for (int i = 1; i < size; i++)    
        ans = gcd(ans, arr[i][0]);
  
    // return hcf of numerator
    return (ans);
}
  
// find lcm of denominator series
int findLcm(int** arr, int size)
{
    // ans contains LCM of arr[0][1], ..arr[i][1]
    int ans = arr[0][1];
    for (int i = 1; i < size; i++)
        ans = (((arr[i][1] * ans)) / 
               (gcd(arr[i][1], ans)));
  
    // return lcm of denominator
    return (ans);
}
  
// Core Function
int* hcfOfFraction(int** arr, int size)
{
    // found hcf of numerator
    int hcf_of_num = findHcf(arr, size);
  
    // found lcm of denominator
    int lcm_of_deno = findLcm(arr, size);
  
    int* result = new int[2];
    result[0] = hcf_of_num;
    result[1] = lcm_of_deno;
  
    for (int i = result[0] / 2; i > 1; i--) 
    {
        if ((result[1] % i == 0) && (result[0] % i == 0))
        {
            result[1] /= i;
            result[0] /= i;
        }
    }
  
    // return result
    return (result);
}
  
// Main function
int main()
{
    int size = 4;
    int** arr = new int*[size];
  
    // Initialize the every row
    // with size 2 (1 for numerator
    // and 2 for denominator)
    for (int i = 0; i < size; i++)
        arr[i] = new int[2];
  
    arr[0][0] = 9;
    arr[0][1] = 10;
    arr[1][0] = 12;
    arr[1][1] = 25;
    arr[2][0] = 18;
    arr[2][1] = 35;
    arr[3][0] = 21;
    arr[3][1] = 40;
      
    // function for calculate the result
    int* result = hcfOfFraction(arr, size);
      
    // print the result
    cout << result[0] << ", " << result[1] << endl;
    return 0;
}

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Java














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// Java program to find HCF of array of  


// rational numbers (fractions). 


class GFG  


{ 


  


// hcf of two number 


static int gcd(int a, int b) 


{ 


    if (a % b == 0) 


        return b; 


    else


        return (gcd(b, a % b)); 


} 


  


// find hcf of numerator series 


static int findHcf(int [][]arr, int size) 


{ 


    int ans = arr[0][0];  


    for (int i = 1; i < size; i++)  


        ans = gcd(ans, arr[i][0]); 


  


    // return hcf of numerator 


    return (ans); 


} 


  


// find lcm of denominator series 


static int findLcm(int[][] arr, int size) 


{ 


    // ans contains LCM of arr[0][1], ..arr[i][1] 


    int ans = arr[0][1]; 


    for (int i = 1; i < size; i++) 


        ans = (((arr[i][1] * ans)) /  


            (gcd(arr[i][1], ans))); 


  


    // return lcm of denominator 


    return (ans); 


} 


  


// Core Function 


static int[] hcfOfFraction(int[][] arr, int size) 


{ 


    // found hcf of numerator 


    int hcf_of_num = findHcf(arr, size); 


  


    // found lcm of denominator 


    int lcm_of_deno = findLcm(arr, size); 


  


    int[] result = new int[2]; 


    result[0] = hcf_of_num; 


    result[1] = lcm_of_deno; 


  


    for (int i = result[0] / 2; i > 1; i--)  


    { 


        if ((result[1] % i == 0) && (result[0] % i == 0)) 


        { 


            result[1] /= i; 


            result[0] /= i; 


        } 


    } 


  


    // return result 


    return (result); 


} 


  


// Driver code 


public static void main(String[] args) 


{ 


    int size = 4; 


    int[][] arr = new int[size][size]; 


  


    // Initialize the every row 


    // with size 2 (1 for numerator 


    // and 2 for denominator) 


    for (int i = 0; i < size; i++) 


        arr[i] = new int[2]; 


  


    arr[0][0] = 9; 


    arr[0][1] = 10; 


    arr[1][0] = 12; 


    arr[1][1] = 25; 


    arr[2][0] = 18; 


    arr[2][1] = 35; 


    arr[3][0] = 21; 


    arr[3][1] = 40; 


      


    // function for calculate the result 


    int[] result = hcfOfFraction(arr, size); 


      


    // print the result 


    System.out.println(result[0] + ", " + result[1]); 


    } 


} 


  


/* This code contributed by PrinciRaj1992 */



















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Python3














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# Python 3 program to find HCF of array of  


from math import gcd 


  


# find hcf of numerator series 


def findHcf(arr, size): 


    ans = arr[0][0]  


    for i in range(1, size, 1): 


        ans = gcd(ans, arr[i][0]) 


  


    # return hcf of numerator 


    return (ans) 


  


# find lcm of denominator series 


def findLcm(arr, size): 


      


    # ans contains LCM of arr[0][1], ..arr[i][1] 


    ans = arr[0][1] 


    for i in range(1, size, 1): 


        ans = int((((arr[i][1] * ans)) /


                (gcd(arr[i][1], ans)))) 


  


    # return lcm of denominator 


    return (ans) 


  


# Core Function 


def hcfOfFraction(arr, size): 


      


    # found hcf of numerator 


    hcf_of_num = findHcf(arr, size) 


  


    # found lcm of denominator 


    lcm_of_deno = findLcm(arr, size) 


  


    result = [0 for i in range(2)] 


    result[0] = hcf_of_num 


    result[1] = lcm_of_deno 


  


    i = int(result[0] / 2) 


    while(i > 1): 


        if ((result[1] % i == 0) and 


            (result[0] % i == 0)): 


            result[1] = int(result[1] / i) 


            result[0] = (result[0] / i) 


  


    # return result 


    return (result) 


  


# Driver Code 


if __name__ == '__main__': 


    size = 4


    arr = [0 for i in range(size)] 


  


    # Initialize the every row 


    # with size 2 (1 for numerator 


    # and 2 for denominator) 


    for i in range(size): 


        arr[i] = [0 for i in range(2)] 


  


    arr[0][0] = 9


    arr[0][1] = 10


    arr[1][0] = 12


    arr[1][1] = 25


    arr[2][0] = 18


    arr[2][1] = 35


    arr[3][0] = 21


    arr[3][1] = 40


      


    # function for calculate the result 


    result = hcfOfFraction(arr, size) 


      


    # print the result 


    print(result[0], ",", result[1]) 


      


# This code is contributed by 


# Surendra_Gangwar 



















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C#














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// C# program to find HCF of array of  


// rational numbers (fractions). 


using System; 


  


class GFG  


{ 


  


// hcf of two number 


static int gcd(int a, int b) 


{ 


    if (a % b == 0) 


        return b; 


    else


        return (gcd(b, a % b)); 


} 


  


// find hcf of numerator series 


static int findHcf(int [,]arr, int size) 


{ 


    int ans = arr[0, 0];  


    for (int i = 1; i < size; i++)  


        ans = gcd(ans, arr[i, 0]); 


  


    // return hcf of numerator 


    return (ans); 


} 


  


// find lcm of denominator series 


static int findLcm(int[,] arr, int size) 


{ 


    // ans contains LCM of arr[0,1], ..arr[i,1] 


    int ans = arr[0,1]; 


    for (int i = 1; i < size; i++) 


        ans = (((arr[i, 1] * ans)) /  


            (gcd(arr[i, 1], ans))); 


  


    // return lcm of denominator 


    return (ans); 


} 


  


// Core Function 


static int[] hcfOfFraction(int[,] arr, int size) 


{ 


    // found hcf of numerator 


    int hcf_of_num = findHcf(arr, size); 


  


    // found lcm of denominator 


    int lcm_of_deno = findLcm(arr, size); 


  


    int[] result = new int[2]; 


    result[0] = hcf_of_num; 


    result[1] = lcm_of_deno; 


  


    for (int i = result[0] / 2; i > 1; i--)  


    { 


        if ((result[1] % i == 0) && (result[0] % i == 0)) 


        { 


            result[1] /= i; 


            result[0] /= i; 


        } 


    } 


  


    // return result 


    return (result); 


} 


  


// Driver code 


public static void Main(String[] args) 


{ 


    int size = 4; 


    int[,] arr = new int[size, size]; 


  


    // Initialize the every row 


    // with size 2 (1 for numerator 


    // and 2 for denominator) 


  


  


    arr[0, 0] = 9; 


    arr[0, 1] = 10; 


    arr[1, 0] = 12; 


    arr[1, 1] = 25; 


    arr[2, 0] = 18; 


    arr[2, 1] = 35; 


    arr[3, 0] = 21; 


    arr[3, 1] = 40; 


      


    // function for calculate the result 


    int[] result = hcfOfFraction(arr, size); 


      


    // print the result 


    Console.WriteLine(result[0] + ", " + result[1]); 


    } 


} 


  


// This code has been contributed by 29AjayKumar 



















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Output:


3, 1400





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