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Content of a Polynomial
• Difficulty Level : Basic
• Last Updated : 22 Apr, 2021

Given an array arr[] which denotes the integer coefficients of the polynomial, the task is to find the content of the polynomial.

Content of polynomials with integer coefficients is defined as the greatest common divisor of its integer coefficients.
That is for:

F(x) = amxm + am-1xm-1 + ……..+a1x + a0
Then, Content of Polynomial = gcd(am, am-1, am-2…., a1, a0)

Examples:

Input: arr[]  = {9, 30, 12}
Output: 3
Explanation:
Given Polynomial can be: 9x2 + 30x + 12
Therefore, Content = gcd(9, 30, 12) = 3

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

Approach: The idea is to find the Greatest common divisor of all the elements of the array which can be computed by finding the GCD repeatedly by choosing two elements at a time. That is:

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

Below is the implementation of the above approach:

## C++

 `// C++ implementation to find the``// content of the polynomial` `#include ``using` `namespace` `std;` `#define newl "\n"``#define ll long long``#define pb push_back` `// Function to find the content``// of the polynomial``int` `findContent(``int` `arr[], ``int` `n)``{``    ``int` `content = arr;` `    ``// Loop to iterate over the``    ``// elements of the array``    ``for` `(``int` `i = 1; i < n; i++) {` `        ``//__gcd(a, b) is a inbuilt``        ``// function for Greatest``        ``// Common Divisor``        ``content = __gcd(content, arr[i]);``    ``}` `    ``return` `content;``}` `// Driver Code``int` `main()``{``    ``int` `n = 3;``    ``int` `arr[] = { 9, 6, 12 };` `    ``// Function call``    ``cout << findContent(arr, n);``    ``return` `0;``}`

## Java

 `// Java implementation to find the``// content of the polynomial``class` `GFG{` `// Function to find the content``// of the polynomial``static` `int` `findContent(``int` `arr[], ``int` `n)``{``    ``int` `content = arr[``0``];` `    ``// Loop to iterate over the``    ``// elements of the array``    ``for``(``int` `i = ``1``; i < n; i++)``    ``{``        ` `        ``//__gcd(a, b) is a inbuilt``        ``// function for Greatest``        ``// Common Divisor``        ``content = __gcd(content, arr[i]);``    ``}``    ``return` `content;``}` `static` `int` `__gcd(``int` `a, ``int` `b)``{``    ``return` `b == ``0` `? a : __gcd(b, a % b);    ``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``3``;``    ``int` `arr[] = { ``9``, ``6``, ``12` `};` `    ``// Function call``    ``System.out.print(findContent(arr, n));``}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 implementation to find the``# content of the polynomial``from` `math ``import` `gcd` `# Function to find the content``# of the polynomial``def` `findContent(arr, n):``    ` `    ``content ``=` `arr[``0``]` `    ``# Loop to iterate over the``    ``# elements of the array``    ``for` `i ``in` `range``(``1``, n):` `        ``# __gcd(a, b) is a inbuilt``        ``# function for Greatest``        ``# Common Divisor``        ``content ``=` `gcd(content, arr[i])` `    ``return` `content` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``n ``=` `3``    ``arr ``=` `[ ``9``, ``6``, ``12` `]` `    ``# Function call``    ``print``(findContent(arr, n))` `# This code is contributed by mohit kumar 29`

## C#

 `// C# implementation to find the``// content of the polynomial``using` `System;` `class` `GFG{` `// Function to find the content``// of the polynomial``static` `int` `findContent(``int` `[]arr, ``int` `n)``{``    ``int` `content = arr;` `    ``// Loop to iterate over the``    ``// elements of the array``    ``for``(``int` `i = 1; i < n; i++)``    ``{``        ` `        ``//__gcd(a, b) is a inbuilt``        ``// function for Greatest``        ``// Common Divisor``        ``content = __gcd(content, arr[i]);``    ``}``    ``return` `content;``}` `static` `int` `__gcd(``int` `a, ``int` `b)``{``    ``return` `b == 0 ? a : __gcd(b, a % b);    ``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 3;``    ``int` `[]arr = { 9, 6, 12 };` `    ``// Function call``    ``Console.Write(findContent(arr, n));``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:
`3`

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