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

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

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

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

 ` `

Output:

```1
```

Time Complexity: O(1)

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