# GCD of more than two (or array) numbers

Given an array of numbers, find GCD of the array elements. In a previous post we find GCD of two number.

Examples:

```Input  : arr[] = {1, 2, 3}
Output : 1

Input  : arr[] = {2, 4, 6, 8}
Output : 2
```

The GCD of three or more numbers equals the product of the prime factors common to all the numbers, but it can also be calculated by repeatedly taking the GCDs of pairs of numbers.

```gcd(a, b, c) = gcd(a, gcd(b, c))
= gcd(gcd(a, b), c)
= gcd(gcd(a, c), b)
```

For an array of elements, we do following.

```result = arr[0]
For i = 1 to n-1
result = GCD(result, arr[i])
```

Below is the implementation of above idea.

## C++

 `// C++ program to find GCD of two or ` `// more numbers ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return gcd of a and b ` `int` `gcd(``int` `a, ``int` `b) ` `{ ` `    ``if` `(a == 0) ` `        ``return` `b; ` `    ``return` `gcd(b % a, a); ` `} ` ` `  `// Function to find gcd of array of ` `// numbers ` `int` `findGCD(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `result = arr[0]; ` `    ``for` `(``int` `i = 1; i < n; i++) ` `        ``result = gcd(arr[i], result); ` ` `  `    ``return` `result; ` `} ` ` `  `// Driven code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 2, 4, 6, 8, 16 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `    ``cout << findGCD(arr, n) << endl; ` `    ``return` `0; ` `} `

## Java

 `// Java program to find GCD of two or ` `// more numbers ` ` `  `public` `class` `GCD { ` `    ``// Function to return gcd of a and b ` `    ``static` `int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(a == ``0``) ` `            ``return` `b; ` `        ``return` `gcd(b % a, a); ` `    ``} ` ` `  `    ``// Function to find gcd of array of ` `    ``// numbers ` `    ``static` `int` `findGCD(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``int` `result = arr[``0``]; ` `        ``for` `(``int` `i = ``1``; i < n; i++) ` `            ``result = gcd(arr[i], result); ` ` `  `        ``return` `result; ` `    ``} ` ` `  `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``2``, ``4``, ``6``, ``8``, ``16` `}; ` `        ``int` `n = arr.length; ` `        ``System.out.println(findGCD(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by Saket Kumar `

## Python

 `# GCD of more than two (or array) numbers ` ` `  `# Function implements the Euclidian  ` `# algorithm to find H.C.F. of two number ` `def` `find_gcd(x, y): ` `     `  `    ``while``(y): ` `        ``x, y ``=` `y, x ``%` `y ` `     `  `    ``return` `x ` `         `  `# Driver Code         ` `l ``=` `[``2``, ``4``, ``6``, ``8``, ``16``] ` ` `  `num1 ``=` `l[``0``] ` `num2 ``=` `l[``1``] ` `gcd ``=` `find_gcd(num1, num2) ` ` `  `for` `i ``in` `range``(``2``, ``len``(l)): ` `    ``gcd ``=` `find_gcd(gcd, l[i]) ` `     `  `print``(gcd) ` ` `  `# Code contributed by Mohit Gupta_OMG `

## C#

 `// C# program to find GCD of  ` `// two or more numbers ` `using` `System; ` ` `  `public` `class` `GCD { ` `     `  `    ``// Function to return gcd of a and b ` `    ``static` `int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(a == 0) ` `            ``return` `b; ` `        ``return` `gcd(b % a, a); ` `    ``} ` ` `  `    ``// Function to find gcd of  ` `    ``// array of numbers ` `    ``static` `int` `findGCD(``int``[] arr, ``int` `n) ` `    ``{ ` `        ``int` `result = arr[0]; ` `        ``for` `(``int` `i = 1; i < n; i++) ` `            ``result = gcd(arr[i], result); ` ` `  `        ``return` `result; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] arr = { 2, 4, 6, 8, 16 }; ` `        ``int` `n = arr.Length; ` `        ``Console.Write(findGCD(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by nitin mittal `

## PHP

 ` `

Output:

```2
```