Ways to express a number as product of two different factors

Given a number n, write a program to calculate number of ways in which number can be expressed as product of two different factors.

Examples :

Input : 12
Output : 3
12 can be expressed as 1 * 12, 2 * 6 and 3*4. 

Input : 36
Output : 4
36 can be expressed as 1 * 36, 2 * 18, 3 * 12 and 4 * 9.




All factors of 12 are = 1, 2, 3, 4, 6, 12

We can observe that factors always exist in
pair which is equal to number.

Here (1, 12), (2, 6) and (3, 4) are such pairs.

As a number can expressed as product of two factors we only need to find number of factors of number upto square root of number. And we only need to find only different pairs so in case of perfect square we don’t include that factor.

C++

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// CPP program to find number of ways
// in which number expressed as
// product of two different factors
#include <bits/stdc++.h>
using namespace std;
  
// To count number of ways in which
// number expressed as product
// of two different numbers
int countWays(int n)
{
    // To store count of such pairs
    int count = 0;
  
    // Counting number of pairs
    // upto sqrt(n) - 1
    for (int i = 1; i * i < n; i++)
        if (n % i == 0)
            count++;
  
    // To return count of pairs
    return count;
}
  
// Driver program to test countWays()
int main()
{
    int n = 12;
    cout << countWays(n) << endl;
    return 0;
}

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Java














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// Java program to find number of ways 


// in which number expressed as 


// product of two different factors 


public class Main { 


  


    // To count number of ways in which 


    // number expressed as product 


    // of two different numbers 


    static int countWays(int n) 


    { 


        // To store count of such pairs 


        int count = 0; 


  


        // Counting number of pairs 


        // upto sqrt(n) - 1 


        for (int i = 1; i * i < n; i++) 


            if (n % i == 0) 


                count++; 


  


        // To return count of pairs 


        return count; 


    } 


  


    // Driver program to test countWays() 


    public static void main(String[] args) 


    { 


        int n = 12; 


        System.out.println(countWays(n)); 


    } 


} 



















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Python 3














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# Python 3 program to find number of ways 


# in which number expressed as 


# product of two different factors 


  


# To count number of ways in which 


# number expressed as product 


# of two different numbers 


def countWays(n): 


      


    # To store count of such pairs 


    count = 0


    i = 1


      


    # Counting number of pairs 


    # upto sqrt(n) - 1 


    while ((i * i)<n) :  


        if(n % i == 0): 


            count += 1    


        i += 1


          


    # To return count of pairs 


    return count 


  


# Driver program to test countWays() 


n = 12


print (countWays(n)) 


  


# This code is contributed 


# by Azkia Anam. 



















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C#














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// C# program to find number of ways 


// in which number expressed as 


// product of two different factors 


using System; 


  


public class main { 


  


    // To count number of ways in which 


    // number expressed as product 


    // of two different numbers 


    static int countWays(int n) 


    { 


  


        // To store count of such pairs 


        int count = 0; 


  


        // Counting number of pairs 


        // upto sqrt(n) - 1 


        for (int i = 1; i * i < n; i++) 


            if (n % i == 0) 


                count++; 


  


        // To return count of pairs 


        return count; 


    } 


  


    // Driver program to test countWays() 


    public static void Main() 


    { 


        int n = 12; 


  


        Console.WriteLine(countWays(n)); 


    } 


} 


  


// This code is contributed by Anant Agarwal. 



















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PHP














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<?php 


// PHP program to find number of ways 


// in which number expressed as 


// product of two different factors 


  


// To count number of ways in which 


// number expressed as product 


// of two different numbers 


function countWays($n) 


{ 


    // To store count of such pairs 


    $count = 0; 


  


    // Counting number of pairs 


    // upto sqrt(n) - 1 


    for ($i = 1; $i * $i < $n; $i++)  


        if ($n % $i == 0) 


            $count++;  


  


    // To return count of pairs 


    return $count; 


} 


  


// Driver Code 


$n = 12; 


echo countWays($n), "\n"; 


  


// This code is contributed by ajit 


?> 



















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Output :


3



This article is contributed by nuclode. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


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