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GCD of elements in a given range

  • Difficulty Level : Medium
  • Last Updated : 21 May, 2021

Given two numbers n and m. Find the biggest integer a(gcd), such that all integers n, n + 1, n + 2, …, m are divisible by a.
Examples: 
 

Input : n = 1, m = 2
Output: 1
Explanation:
Here, series become 1, 2. So, the 
greatest no which divides both of 
them is 1.

Input : n = 475, m = 475
Output : 475
Explanation:
Here, series has only one term 475.
So, greatest no which divides 475 is 475.

 

Here, We have to examine only two cases: 
 

  1. if a = b : the segment consists of a single number, hence the answer is a.
  2. if a < b : we have gcd(n, n + 1, n?+ 2, …, m) = gcd(gcd(n, n + 1), n + 2, …, m) = gcd(1, n + 2, …, n) = 1.

C++




// GCD of given range
#include <bits/stdc++.h>
using namespace std;
   
int rangeGCD(int n, int m)
{
    return (n == m)? n : 1;
}
   
int main()
{
    int n = 475;
    int m = 475;
    cout << rangeGCD(n, m);
    return 0;
}

Java




// GCD of given range
   
import java.io.*;
   
class GFG {
   
    static int rangeGCD(int n, int m)
    {
        return (n == m) ? n : 1;
    }
   
    public static void main(String[] args)
    {
        int n = 475;
        int m = 475;
           
        System.out.println(rangeGCD(n, m));
    }
}
   
// This code is contributed by Ajit.

Python3




# GCD of given range
   
def rangeGCD(n, m):
    return n if(n == m) else 1
       
# Driver code
n, m = 475, 475
print(rangeGCD(n, m))
   
# This code is contributed by Anant Agarwal.

C#




// GCD of given range
using System;
    
class GFG {
    
    static int rangeGCD(int n, int m)
    {
        return (n == m) ? n : 1;
    }
    
    public static void Main()
    {
        int n = 475;
        int m = 475;
            
        Console.WriteLine(rangeGCD(n, m));
    }
}
    
// This code is contributed by Anant Agarwal.

PHP




<?php
// PHP program for
// GCD of given range
   
// function returns the GCD
function rangeGCD($n, $m)
{
    return ($n == $m)? $n : 1;
}
   
    // Driver Code
    $n = 475;
    $m = 475;
    echo rangeGCD($n, $m);
       
// This code is contributed by anuj_67.
?>

Javascript




<script>
 
// GCD of given range
 
    
    function rangeGCD( n,  m)
    {
        return (n == m) ? n : 1;
    }
    
 
        var n = 475;
        var m = 475;
            
        document.write(rangeGCD(n, m));
 
 
</script>

Output:

475

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