Print all numbers whose set of prime factors is a subset of the set of the prime factors of X

Given a number X and an array of N numbers. The task is to print all the numbers in the array whose set of prime factors is a subset of the set of the prime factors of X.

Examples:

Input: X = 60, a[] = {2, 5, 10, 7, 17}
Output: 2 5 10
Set of prime factors of 60: {2, 3, 5}

Set of prime factors of 2: {2}
Set of prime factors of 5: {5}
Set of prime factors of 10: {2, 5}
Set of prime factors of 7: {7}
Set of prime factors of 17: {17}
Hence only 2, 5 and 10’s set of prime factors is a subset of set of prime
factors of 60.

Input: X = 15, a[] = {2, 8}
Output: There are no such numbers

Approach: Iterate for every element in the array, and keep dividing the number by the gcd of the number and X till gcd becomes 1 for the number and X. If at the end the number becomes 1 after continous division, then print that number.

Below is the implementation of the above approach:

C++

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// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to print all the numbers
void printNumbers(int a[], int n, int x)
{
  
    bool flag = false;
  
    // Iterate for every element in the array
    for (int i = 0; i < n; i++) {
  
        int num = a[i];
  
        // Find the gcd
        int g = __gcd(num, x);
  
        // Iterate till gcd is 1
        // of number and x
        while (g != 1) {
  
            // Divide the number by gcd
            num /= g;
  
            // Find the new gcdg
            g = __gcd(num, x);
        }
  
        // If the number is 1 at the end
        // then print the number
        if (num == 1) {
            flag = true;
            cout << a[i] << " ";
        }
    }
  
    // If no numbers have been there
    if (!flag)
        cout << "There are no such numbers";
}
  
// Drivers code
int main()
{
    int x = 60;
    int a[] = { 2, 5, 10, 7, 17 };
    int n = sizeof(a) / sizeof(a[0]);
  
    printNumbers(a, n, x);
    return 0;
}

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Java

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// Java program to implement
// the above approach
class GFG
{
  
// Function to print all the numbers
static void printNumbers(int a[], int n, int x)
{
  
    boolean flag = false;
  
    // Iterate for every element in the array
    for (int i = 0; i < n; i++) 
    {
  
        int num = a[i];
  
        // Find the gcd
        int g = __gcd(num, x);
  
        // Iterate till gcd is 1
        // of number and x
        while (g != 1)
        {
  
            // Divide the number by gcd
            num /= g;
  
            // Find the new gcdg
            g = __gcd(num, x);
        }
  
        // If the number is 1 at the end
        // then print the number
        if (num == 1
        {
            flag = true;
            System.out.print(a[i] + " ");
        }
    }
  
    // If no numbers have been there
    if (!flag)
        System.out.println("There are no such numbers");
}
  
static int __gcd(int a, int b) 
    if (b == 0
        return a; 
    return __gcd(b, a % b); 
      
}
  
// Drivers code
public static void main(String[] args)
{
    int x = 60;
    int a[] = { 2, 5, 10, 7, 17 };
    int n = a.length;
  
    printNumbers(a, n, x);
}
}
  
/* This code contributed by PrinciRaj1992 */

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Python3

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# Python3 program to implement 
# the above approach 
from math import gcd
  
# Function to print all the numbers 
def printNumbers(a, n, x) : 
  
    flag = False
  
    # Iterate for every element in the array 
    for i in range(n) :
  
        num = a[i]
  
        # Find the gcd 
        g = gcd(num, x)
  
        # Iterate till gcd is 1 
        # of number and x 
        while (g != 1) : 
  
            # Divide the number by gcd 
            num //= g
  
            # Find the new gcdg 
            g = gcd(num, x)
  
        # If the number is 1 at the end 
        # then print the number 
        if (num == 1) :
            flag = True
            print(a[i], end = " ");
  
    # If no numbers have been there 
    if (not flag) :
        print("There are no such numbers"
  
# Driver Code 
if __name__ == "__main__"
  
    x = 60
    a = [ 2, 5, 10, 7, 17 ]
    n = len(a) 
  
    printNumbers(a, n, x)
      
# This code is contributed by Ryuga

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C#

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// C# program to implement
// the above approach
using System;
  
class GFG
{
  
// Function to print all the numbers
static void printNumbers(int []a, int n, int x)
{
  
    bool flag = false;
  
    // Iterate for every element in the array
    for (int i = 0; i < n; i++) 
    {
  
        int num = a[i];
  
        // Find the gcd
        int g = __gcd(num, x);
  
        // Iterate till gcd is 1
        // of number and x
        while (g != 1)
        {
  
            // Divide the number by gcd
            num /= g;
  
            // Find the new gcdg
            g = __gcd(num, x);
        }
  
        // If the number is 1 at the end
        // then print the number
        if (num == 1) 
        {
            flag = true;
            Console.Write(a[i] + " ");
        }
    }
  
    // If no numbers have been there
    if (!flag)
        Console.WriteLine("There are no such numbers");
}
  
static int __gcd(int a, int b) 
    if (b == 0) 
        return a; 
    return __gcd(b, a % b); 
      
}
  
// Driver code
public static void Main(String[] args)
{
    int x = 60;
    int []a = { 2, 5, 10, 7, 17 };
    int n = a.Length;
  
    printNumbers(a, n, x);
}
}
  
// This code has been contributed by 29AjayKumar

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PHP

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<?php
// PHP program to implement
// the above approach
  
// Function to print all the numbers
function printNumbers($a, $n, $x)
{
  
    $flag = false;
  
    // Iterate for every element in the array
    for ($i = 0; $i < $n; $i++) 
    {
  
        $num = $a[$i];
  
        // Find the gcd
        $g = __gcd($num, $x);
  
        // Iterate till gcd is 1
        // of number and x
        while ($g != 1)
        {
  
            // Divide the number by gcd
            $num /= $g;
  
            // Find the new gcdg
            $g = __gcd($num, $x);
        }
  
        // If the number is 1 at the end
        // then print the number
        if ($num == 1) 
        {
            $flag = true;
            echo $a[$i] , " ";
        }
    }
  
    // If no numbers have been there
    if (!$flag)
        echo ("There are no such numbers");
}
  
function __gcd($a, $b
    if ($b == 0) 
        return $a
    return __gcd($b, $a % $b); 
      
}
  
// Driver code
  
$x = 60;
$a = array(2, 5, 10, 7, 17 );
$n = count($a);
  
  
printNumbers($a, $n, $x);
  
// This code has been contributed by ajit.
?>

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Output:

2 5 10


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Striver(underscore)79 at Codechef and codeforces D

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