# Greatest divisor which divides all natural number in range [L, R]

• Difficulty Level : Easy
• Last Updated : 15 Apr, 2021

Given two integers L and R, the task is to find the greatest divisor that divides all the natural numbers in the range [L, R].
Examples:

Input: L = 3, R = 12
Output: 1
Input: L = 24, R = 24
Output: 24

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Approach: For a range of consecutive integer elements, there are two cases:

• If L = R then the answer will L.
• If L < R then all consecutive natural numbers in this range are co-primes. So, 1 is the only number that will be able to divide all the elements of the range.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the greatest divisor that``// divides all the natural numbers in the range [l, r]``int` `find_greatest_divisor(``int` `l, ``int` `r)``{``    ``if` `(l == r)``        ``return` `l;` `    ``return` `1;``}` `// Driver Code``int` `main()``{``    ``int` `l = 2, r = 12;` `    ``cout << find_greatest_divisor(l, r);``}`

## Java

 `// Java implementation of the approach` `class` `GFG {` `// Function to return the greatest divisor that``// divides all the natural numbers in the range [l, r]``    ``static` `int` `find_greatest_divisor(``int` `l, ``int` `r) {``        ``if` `(l == r) {``            ``return` `l;``        ``}` `        ``return` `1``;``    ``}` `// Driver Code``    ``public` `static` `void` `main(String[] args) {``        ``int` `l = ``2``, r = ``12``;` `        ``System.out.println(find_greatest_divisor(l, r));``    ``}``}``// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 implementation of the approach` `# Function to return the greatest divisor that``# divides all the natural numbers in the range [l, r]``def` `find_greatest_divisor(l, r):` `    ``if` `(l ``=``=` `r):``        ``return` `l;` `    ``return` `1``;`  `# Driver Code` `l ``=` `2``;``r ``=` `12``;` `print``(find_greatest_divisor(l, r));` `#This code is contributed by Shivi_Aggarwal`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG {` `    ``// Function to return the greatest divisor that``    ``// divides all the natural numbers in the range [l, r]``    ``static` `int` `find_greatest_divisor(``int` `l, ``int` `r) {``        ``if` `(l == r) {``            ``return` `l;``        ``}` `        ``return` `1;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main() {``        ``int` `l = 2,  r = 12 ;` `        ``Console.WriteLine(find_greatest_divisor(l, r));``    ``}``    ``// This code is contributed by Ryuga` `}`

## PHP

 ``

## Javascript

 ``
Output:
`1`

Time Complexity: O(1)

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