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# Distinct Prime Factors of an Array

Given an array arr[] of size N, the task is to find the distinct prime factors of all the numbers in the given array.

Examples:

Input: N = 3, arr[] = {12, 15, 18}
Output: 2 3 5
Explanation:
12 = 2 x 2 x 3
15 = 3 x 5
18 = 2 x 3 x 3
Distinct prime factors among the given numbers are 2, 3, 5.

Input: N = 9, arr[] = {2, 3, 4, 5, 6, 7, 8, 9, 10}
Output: 2 3 5 7

Naive Approach: A simple approach of this problem will be finding the prime factors of each number in the array. Then find the distinct prime numbers among these prime factors.
Time Complexity: O(N2)

Efficient Approach: An efficient approach is to first find all prime numbers up to the given limit using Sieve of Eratosthenes and store them in an array. For every prime number in the prime array, check if any number in the input array is divisible or not. If it is divisible, then store that prime number in the answer array. Finally, return the answer array after repeating this process for all the numbers in the given input array.

Below is the implementation of the above approach:

## C++14

 `#include `   `using` `namespace` `std;`   `//cppimplementation of the above approach`   `//Function to return an array` `//of prime numbers upto n` `//using Sieve of Eratosthenes` `vector<``int``> sieve(``int` `n){` `    ``vector<``int``> prime (n + 1,0);` `    ``int` `p = 2;` `    ``while``(p * p<= n){` `        ``if``(prime[p]== 0){` `            ``for` `(``int` `i=2*p;i allPrimes;` `    ``for` `(``int` `i =2;i distPrime(vector<``int``> arr, vector<``int``> allPrimes){`   `    ``//Creating an empty array` `    ``//to store distinct prime factors` `    ``vector<``int``> list1;`   `    ``//Iterating through all the` `    ``//prime numbers and check if` `    ``//any of the prime numbers is a` `    ``//factor of the given input array` `    ``for` `(``int` `i : allPrimes){` `        ``for` `(``int` `j :arr){` `            ``if``(j % i == 0){` `                ``list1.push_back(i);` `                ``break``;` `              ``}` `            ``}` `          ``}` `    ``return` `list1;` `  ``}`   `//Driver code`   `int` `main()` `{` `  ``//Finding prime numbers upto 10000` `  ``//using Sieve of Eratosthenes` `  ``vector<``int``> allPrimes = sieve(10000);`   `  ``vector<``int``> arr = {15, 30, 60};` `  ``vector<``int``> ans = distPrime(arr, allPrimes);` `  ``cout<<``"["``;` `  ``for``(``int` `i:ans) cout<

## Java

 `// Java implementation of the above approach` `import` `java.util.*;`   `class` `GFG` `{`   `// Function to return an array` `// of prime numbers upto n` `// using Sieve of Eratosthenes` `static` `ArrayList sieve(``int` `n){` `    ``ArrayList prime = ``new` `ArrayList();` `    ``for``(``int` `i = ``0``; i < n + ``1``; i++)` `    ``prime.add(``0``);` `    ``int` `p = ``2``;` `    ``while``(p * p <= n){` `        ``if``(prime.get(p) == ``0``){` `            ``for` `(``int` `i = ``2` `* p; i < n + ``1``; i += p)` `                ``prime.set(i, ``1``);` `            ``}` `        ``p += ``1``;` `    ``}`   `    ``ArrayList allPrimes = ``new` `ArrayList();` `    ``for` `(``int` `i = ``2``; i < n; i++){` `    ``if` `(prime.get(i) == ``0``)` `        ``allPrimes.add(i);` `    ``}` `    ``return` `allPrimes;` `}`   `// Function to return distinct` `// prime factors from the given array` `static` `ArrayList distPrime(ArrayList arr, ` `                            ``ArrayList allPrimes){`   `    ``// Creating an empty array` `    ``// to store distinct prime factors` `    ``ArrayList list1 = ``new` `ArrayList();`   `    ``// Iterating through all the` `    ``// prime numbers and check if` `    ``// any of the prime numbers is a` `    ``// factor of the given input array` `    ``for` `(``int` `i = ``0``; i < allPrimes.size(); i++){` `        ``for` `(``int` `j = ``0``; j < arr.size(); j++){` `            ``if``(arr.get(j) % allPrimes.get(i) == ``0``){` `                ``list1.add(allPrimes.get(i));` `                ``break``;` `            ``}` `            ``}` `        ``}` `    ``return` `list1;` `}`   `// Driver code` `public` `static` `void` `main(String args[])` `{` `    `  `    ``// Finding prime numbers upto 10000` `    ``// using Sieve of Eratosthenes` `    ``ArrayList allPrimes = ``new` `ArrayList(sieve(``10000``));` `    ``ArrayList arr = ``new` `ArrayList();` `    ``arr.add(``15``);` `    ``arr.add(``30``);` `    ``arr.add(``60``);` `    ``ArrayList ans = ``new` `ArrayList(distPrime(arr, allPrimes));` `    ``System.out.print(``"["``);` `    ``for``(``int` `i = ``0``; i < ans.size(); i++)` `    ``System.out.print(ans.get(i) + ``" "``);` `    ``System.out.print(``"]"``);` `}` `}`   `// This code is contributed by Surendra_Gangwar`

## Python3

 `# Python3 implementation of the above approach`   `# Function to return an array ` `# of prime numbers upto n ` `# using Sieve of Eratosthenes` `def` `sieve(n):` `    ``prime ``=``[``True``]``*``(n ``+` `1``)` `    ``p ``=` `2` `    ``while``(p ``*` `p<``=` `n):` `        ``if``(prime[p] ``=``=` `True``):` `            ``for` `i ``in` `range``(p ``*` `p, n ``+` `1``, p):` `                ``prime[i] ``=` `False` `        ``p ``+``=` `1` `    ``allPrimes ``=` `[x ``for` `x ``in` `range``(``2``, n)``if` `prime[x]]` `    ``return` `allPrimes`   `# Function to return distinct ` `# prime factors from the given array ` `def` `distPrime(arr, allPrimes):`   `    ``# Creating an empty array` `    ``# to store distinct prime factors` `    ``list1 ``=` `list``()` `    `  `    ``# Iterating through all the ` `    ``# prime numbers and check if ` `    ``# any of the prime numbers is a` `    ``# factor of the given input array` `    ``for` `i ``in` `allPrimes:` `        ``for` `j ``in` `arr:` `            ``if``(j ``%` `i ``=``=` `0``):` `                ``list1.append(i)` `                ``break` `    ``return` `list1`   `# Driver code` `if` `__name__``=``=``"__main__"``:`   `    ``# Finding prime numbers upto 10000` `    ``# using Sieve of Eratosthenes` `    ``allPrimes ``=` `sieve(``10000``)`   `    ``arr ``=` `[``15``, ``30``, ``60``]` `    ``ans ``=` `distPrime(arr, allPrimes)` `    ``print``(ans)`   `# This code is contributed by mohit kumar 29`

## C#

 `// C# implementation of the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG` `{`   `// Function to return an array` `// of prime numbers upto n` `// using Sieve of Eratosthenes` `static` `List<``int``> sieve(``int` `n)` `{` `    ``List<``int``> prime = ``new` `List<``int``>();` `    ``for``(``int` `i = 0; i < n + 1; i++)` `    ``prime.Add(0);` `    ``int` `p = 2;` `    ``while``(p * p <= n)` `    ``{` `        ``if``(prime[p] == 0)` `        ``{` `            ``for` `(``int` `i = 2 * p; i < n + 1; i += p)` `                ``prime[i]= 1;` `            ``}` `        ``p += 1;` `    ``}`   `    ``List<``int``> allPrimes = ``new` `List<``int``>();` `    ``for` `(``int` `i = 2; i < n; i++){` `    ``if` `(prime[i] == 0)` `        ``allPrimes.Add(i);` `    ``}` `    ``return` `allPrimes;` `}`   `// Function to return distinct` `// prime factors from the given array` `static` `List<``int``> distPrime(List<``int``> arr, ` `                            ``List<``int``> allPrimes){`   `    ``// Creating an empty array` `    ``// to store distinct prime factors` `       ``List<``int``> list1 = ``new` `List<``int``>();`   `    ``// Iterating through all the` `    ``// prime numbers and check if` `    ``// any of the prime numbers is a` `    ``// factor of the given input array` `    ``for` `(``int` `i = 0; i < allPrimes.Count; i++){` `        ``for` `(``int` `j = 0; j < arr.Count; j++){` `            ``if``(arr[j] % allPrimes[i] == 0){` `                ``list1.Add(allPrimes[i]);` `                ``break``;` `            ``}` `            ``}` `        ``}` `    ``return` `list1;` `}`   `// Driver code` `public` `static` `void` `Main(``string` `[]args)` `{` `    `  `    ``// Finding prime numbers upto 10000` `    ``// using Sieve of Eratosthenes` `    ``List<``int``> allPrimes = ``new` `List<``int``>(sieve(10000));` `    ``List<``int``> arr = ``new` `List<``int``>();` `    ``arr.Add(15);` `    ``arr.Add(30);` `    ``arr.Add(60);` `    ``List<``int``> ans = ``new` `List<``int``>(distPrime(arr, allPrimes));` `    ``Console.Write(``"["``);` `    ``for``(``int` `i = 0; i < ans.Count; i++)` `    ``Console.Write(ans[i] + ``" "``);` `    ``Console.Write(``"]"``);` `}` `}`   `// This code is contributed by chitranayal`

## Javascript

 ``

Output:

`[2, 3, 5]`

Auxiliary Space: O(10000 + |arr|)

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