Count common prime factors of two numbers

Last Updated : 25 Jun, 2022

Given two integer $A$ and $B$ , the task is to find the count of common factors of two numbers where factors are prime.
Examples:

Input: A = 6, B = 12
Output: 2
2 and 3 are the only common prime divisors of 6 and 12
Input: A = 4, B = 8
Output: 1

Naive Approach: Iterate from 1 to min(A, B) and check whether i is prime and a factor of both A and B, if yes then increment the counter.
Efficient Approach is to do following:

Find Greatest Common Divisor (gcd) of the given numbers.
Find prime factors of the GCD.

Below is the implementation of the above approach:

C++

// CPP program to count common prime factors
// of a and b.
#include <bits/stdc++.h>
using namespace std;
 
// A function to count all prime factors of
// a given number x
int countPrimeFactors(int x)
{
    int res = 0;
    if (x % 2 == 0) {
        res++;
 
        // Print the number of 2s that divide x
        while (x % 2 == 0)
            x = x / 2;
    }
 
    // x must be odd at this point.  So we 
    // can skip one element (Note i = i +2)
    for (int i = 3; i <= sqrt(x); i = i + 2) {
        if (x % i == 0) {
 
            // While i divides x, print i and 
            // divide x
            res++;
            while (x % i == 0)
                x = x / i;
        }
    }
 
    // This condition is to handle the case 
    // when x is a prime number greater than 2
    if (x > 2)
        res++;
    return res;
}
 
// Count of common prime factors
int countCommonPrimeFactors(int a, int b)
{
    // Get the GCD of the given numbers
    int gcd = __gcd(a, b);
 
    // Count prime factors in GCD
    return countPrimeFactors(gcd);
}
 
// Driver code
int main()
{
    int a = 6, b = 12;
    cout << countCommonPrimeFactors(a, b);
    return 0;
}

C

// C program to count common prime factors
// of a and b.
#include <stdio.h>
#include <math.h>
 
// A function to count all prime factors of
// a given number x
int countPrimeFactors(int x)
{
    int res = 0;
    if (x % 2 == 0) {
        res++;
       
        // Print the number of 2s that divide x
        while (x % 2 == 0)
            x = x / 2;
    }
 
    // x must be odd at this point.  So we 
    // can skip one element (Note i = i +2)
    for (int i = 3; i <= sqrt(x); i = i + 2) {
        if (x % i == 0) {
 
            // While i divides x, print i and 
            // divide x
            res++;
            while (x % i == 0)
                x = x / i;
        }
    }
 
    // This condition is to handle the case 
    // when x is a prime number greater than 2
    if (x > 2)
        res++;
    return res;
}
 
// Count of common prime factors
int countCommonPrimeFactors(int a, int b)
{
    int gcd, i;
   
    // Get the GCD of the given numbers
    for(i = 1; i <= a && i <= b; ++i)
    {
        // Checks if i is factor of both integers
        if(a % i == 0 && b % i == 0)
            gcd = i;
    }
 
    // Count prime factors in GCD
    return countPrimeFactors(gcd);
}
 
// Driver code
int main()
{
    int a = 6, b = 12;
    printf("%d",countCommonPrimeFactors(a, b));
    return 0;
}
 
// This code is contributed by kothavvsaakash.

Java

// Java  program to count common prime factors
 // of a and b.
 
import java.io.*;
 
class GFG {
    // Recursive function to return gcd of a and b 
    static int __gcd(int a, int b) 
    { 
        // Everything divides 0  
        if (a == 0) 
          return b; 
        if (b == 0) 
          return a; 
        
        // base case 
        if (a == b) 
            return a; 
        
        // a is greater 
        if (a > b) 
            return __gcd(a-b, b); 
        return __gcd(a, b-a); 
    } 
// A function to count all prime factors of
// a given number x
 static int countPrimeFactors(int x)
{
    int res = 0;
    if (x % 2 == 0) {
        res++;
 
        // Print the number of 2s that divide x
        while (x % 2 == 0)
            x = x / 2;
    }
 
    // x must be odd at this point. So we 
    // can skip one element (Note i = i +2)
    for (int i = 3; i <= Math.sqrt(x); i = i + 2) {
        if (x % i == 0) {
 
            // While i divides x, print i and 
            // divide x
            res++;
            while (x % i == 0)
                x = x / i;
        }
    }
 
    // This condition is to handle the case 
    // when x is a prime number greater than 2
    if (x > 2)
        res++;
    return res;
}
 
// Count of common prime factors
static int countCommonPrimeFactors(int a, int b)
{
    // Get the GCD of the given numbers
    int gcd = __gcd(a, b);
 
    // Count prime factors in GCD
    return countPrimeFactors(gcd);
}
 
// Driver code
 
 
    public static void main (String[] args) {
    int a = 6, b = 12;
    System.out.println(countCommonPrimeFactors(a, b));
    }
}
// This code is contributed by inder_verma..

Python3

# Python 3 program to count common prime 
# factors of a and b.
from math import sqrt,gcd
 
# A function to count all prime 
# factors of a given number x
def countPrimeFactors(x):
    res = 0
    if (x % 2 == 0):
        res += 1
 
        # Print the number of 2s that divide x
        while (x % 2 == 0):
            x = x / 2
 
    # x must be odd at this point. So we 
    # can skip one element (Note i = i +2)
    k = int(sqrt(x)) + 1
    for i in range(3, k, 2):
        if (x % i == 0):
             
            # While i divides x, print i 
            # and divide x
            res += 1
            while (x % i == 0):
                x = x / i
     
    # This condition is to handle the 
    # case when x is a prime number
    # greater than 2
    if (x > 2):
        res += 1
    return res
 
# Count of common prime factors
def countCommonPrimeFactors(a, b):
     
    # Get the GCD of the given numbers
    gcd__ = gcd(a, b)
 
    # Count prime factors in GCD
    return countPrimeFactors(gcd__)
 
# Driver code
if __name__ == '__main__':
    a = 6
    b = 12
    print(countCommonPrimeFactors(a, b))
     
# This code is contributed by
# Surendra_Gangwar

C#

// C# program to count common prime factors 
// of a and b. 
 
using System ;
 
class GFG { 
    // Recursive function to return gcd of a and b 
    static int __gcd(int a, int b) 
    { 
        // Everything divides 0 
        if (a == 0) 
        return b; 
        if (b == 0) 
        return a; 
         
        // base case 
        if (a == b) 
            return a; 
         
        // a is greater 
        if (a > b) 
            return __gcd(a-b, b); 
        return __gcd(a, b-a); 
    } 
    // A function to count all prime factors of 
    // a given number x 
    static int countPrimeFactors(int x) 
    { 
        int res = 0; 
        if (x % 2 == 0) { 
            res++; 
     
            // Print the number of 2s that divide x 
            while (x % 2 == 0) 
                x = x / 2; 
        } 
     
        // x must be odd at this point. So we 
        // can skip one element (Note i = i +2) 
        for (int i = 3; i <= Math.Sqrt(x); i = i + 2) { 
            if (x % i == 0) { 
     
                // While i divides x, print i and 
                // divide x 
                res++; 
                while (x % i == 0) 
                    x = x / i; 
            } 
        } 
     
        // This condition is to handle the case 
        // when x is a prime number greater than 2 
        if (x > 2) 
            res++; 
        return res; 
    } 
     
    // Count of common prime factors 
    static int countCommonPrimeFactors(int a, int b) 
    { 
        // Get the GCD of the given numbers 
        int gcd = __gcd(a, b); 
     
        // Count prime factors in GCD 
        return countPrimeFactors(gcd); 
    } 
     
    // Driver code 
    public static void Main() { 
    int a = 6, b = 12; 
     
    Console.WriteLine(countCommonPrimeFactors(a, b)); 
    } 
    // This code is contributed by Ryuga 
} 

PHP

<?php
// PHP program to count common 
// prime factors of a and b. 
 
// Recursive function to return
// gcd of a and b 
function __gcd($a, $b) 
{ 
    // Everything divides 0 
    if ($a == 0) 
        return $b; 
    if ($b == 0) 
        return $a; 
     
    // base case 
    if ($a == $b) 
        return $a; 
     
    // a is greater 
    if ($a > $b) 
        return __gcd(($a - $b), $b); 
    return __gcd($a, ($b - $a)); 
} 
 
// A function to count all prime 
// factors of a given number x 
function countPrimeFactors($x) 
{ 
    $res = 0; 
    if ($x % 2 == 0)
    { 
        $res++; 
 
        // Print the number of 2s that 
        // divide x 
        while ($x % 2 == 0) 
            $x = $x / 2; 
    } 
 
    // x must be odd at this point. So we 
    // can skip one element (Note i = i +2) 
    for ($i = 3; $i <= sqrt($x); $i = $i + 2) 
    { 
        if ($x % $i == 0) 
        { 
 
            // While i divides x, print i 
            // and divide x 
            $res++; 
            while ($x % $i == 0) 
                $x = $x / $i; 
        } 
    } 
 
    // This condition is to handle the case 
    // when x is a prime number greater than 2 
    if ($x > 2) 
        $res++; 
    return $res; 
} 
 
// Count of common prime factors 
function countCommonPrimeFactors($a, $b) 
{ 
    // Get the GCD of the given numbers 
    $gcd = __gcd($a, $b); 
 
    // Count prime factors in GCD 
    return countPrimeFactors($gcd); 
} 
 
// Driver code 
$a = 6;
$b = 12; 
 
echo (countCommonPrimeFactors($a, $b)); 
 
// This code is contributed by akt_mit..
?>

Javascript

<script>
 
    // Javascript program to count 
    // common prime factors of a and b.
     
    // Recursive function to return 
    // gcd of a and b 
    function __gcd(a, b) 
    { 
        // Everything divides 0 
        if (a == 0) 
            return b; 
        if (b == 0) 
            return a; 
           
        // base case 
        if (a == b) 
            return a; 
           
        // a is greater 
        if (a > b) 
            return __gcd(a-b, b); 
        return __gcd(a, b-a); 
    } 
    // A function to count all prime factors of 
    // a given number x 
    function countPrimeFactors(x) 
    { 
        let res = 0; 
        if (x % 2 == 0) { 
            res++; 
       
            // Print the number of 2s that divide x 
            while (x % 2 == 0) 
                x = parseInt(x / 2, 10); 
        } 
       
        // x must be odd at this point. So we 
        // can skip one element (Note i = i +2) 
        for (let i = 3; i <= Math.sqrt(x); i = i + 2) 
        { 
            if (x % i == 0) { 
       
                // While i divides x, print i and 
                // divide x 
                res++; 
                while (x % i == 0) 
                    x = parseInt(x / i, 10); 
            } 
        } 
       
        // This condition is to handle the case 
        // when x is a prime number greater than 2 
        if (x > 2) 
            res++; 
        return res; 
    } 
       
    // Count of common prime factors 
    function countCommonPrimeFactors(a, b) 
    { 
        // Get the GCD of the given numbers 
        let gcd = __gcd(a, b); 
       
        // Count prime factors in GCD 
        return countPrimeFactors(gcd); 
    } 
     
    let a = 6, b = 12; 
       
    document.write(countCommonPrimeFactors(a, b));
     
</script>

Output:

Time Complexity: O(sqrtn*logn)

Auxiliary Space: O(1)

If there are multiple queries for counting common divisors, we can further optimize above code using Prime Factorization using Sieve O(log n) for multiple queries

Suggest improvement

Digits of element wise sum of two arrays into a new array

unordered_map reserve() in C++ STL

Share your thoughts in the comments

Count common prime factors of two numbers

C++

C

Java

Python3

C#

PHP

Javascript

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