# GCD of elements in a given range

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.
```

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

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.
3. Below is the code for above approach.

## C++

 `// GCD of given range ` `#include ` `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

 ` `

Output:

```475
```

My Personal Notes arrow_drop_up If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : vt_m

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.