# Number of Co-prime pairs from 1 to N with product equals to N

Given a number N. The task is to find the number of co-prime pairs (a, b) from 1 to N such that their product(a*b) is equal to N.

Note: A pair(a, b) is said to be co-prime if gcd(a, b) = 1.

Examples:

Input: N = 120
Output: No. of co-prime pairs = 3
(3, 40)
(5, 24)
(8, 15)

Input: N= 250
Output: No. of co-prime pairs = 3
(2, 125)


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Given that the elements in the pair should be co-prime to each other. Let a co prime pair be (a, b),
Given, a * b = N.

Therefore, So the idea is to run a loop from 1 to and check whether i and (N/i) are coprime to each other or not and whether, i*(N/i) = N. If yes, then count such pairs.

Below is the implementation of the above approach:

## C++

 // C++ program to count number of Co-prime pairs  // from 1 to N with product equals to N  #include  using namespace std;     // Function to count number of Co-prime pairs  // from 1 to N with product equals to N  void countCoprimePairs(int n)  {      int count = 0;         cout << "The co- prime pairs are: " << endl;         // find all the co- prime pairs      // Traverse from 2 to sqrt(N) and check      // if i, N/i are coprimes      for (int i = 2; i <= sqrt(n); i++) {             // check if N is divisible by i,          // so that the other term in pair i.e. N/i          // is integral          if (n % i == 0) {                 // Check if i and N/i are coprime              if (__gcd(i, (n / i)) == 1) {                     // Display the co- prime pairs                  cout << "(" << i << ", " << (n / i) << ")\n";                  count++;              }          }      }         cout << "\nNumber of coprime pairs : " << count;  }     // Driver code  int main()  {      int N = 120;         countCoprimePairs(N);         return 0;  }

## Java

 // Java program to count number of Co-prime pairs  // from 1 to N with product equals to N  import java.io.*;     public 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);       }      // Function to count number of Co-prime pairs  // from 1 to N with product equals to N  static void countCoprimePairs(int n)  {      int count = 0;         System.out.println( "The co- prime pairs are: ");         // find all the co- prime pairs      // Traverse from 2 to sqrt(N) and check      // if i, N/i are coprimes      for (int i = 2; i <= Math.sqrt(n); i++) {             // check if N is divisible by i,          // so that the other term in pair i.e. N/i          // is integral          if (n % i == 0) {                 // Check if i and N/i are coprime              if (__gcd(i, (n / i)) == 1) {                     // Display the co- prime pairs                  System.out.print( "(" +i + ", " + (n / i) + ")\n");                  count++;              }          }      }         System.out.println("\nNumber of coprime pairs : " + count);  }     // Driver code      public static void main (String[] args) {              int N = 120;         countCoprimePairs(N);      }  }     // This code is contributed by shs..

## Python 3

 # Python program to count number   # of Co-prime pairs from 1 to N   # with product equals to N      # import everything from math lib  from math import *    # Function to count number of   # Co-prime pairs from 1 to N  # with product equals to N   def countCoprimePairs(n) :         count = 0        print("The co-prime pairs are: ")         # find all the co- prime pairs       # Traverse from 2 to sqrt(N) and       # check if i, N//i are coprimes       for i in range(2, int(sqrt(n)) + 1) :             # check if N is divisible by i,           # so that the other term in pair           # i.e. N/i is integral           if n % i == 0 :                 # Check if i and N/i are coprime               if gcd(i, n // i) == 1 :                     # Display the co- prime pairs                   print("(", i,",", (n // i),")")                  count += 1        print("Number of coprime pairs : ", count)                     # Driver code       if __name__ == "__main__" :         N = 120        countCoprimePairs(N)     # This code is contributed by ANKITRAI1

## C#

 // C# program to count number   // of Co-prime pairs from 1 to N   // with product equals to N  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);   }      // Function to count number of   // Co-prime pairs from 1 to N   // with product equals to N  static void countCoprimePairs(int n)  {  int count = 0;     Console.WriteLine("The co- prime pairs are: ");     // find all the co- prime pairs  // Traverse from 2 to sqrt(N) and   // check if i, N/i are coprimes  for (int i = 2; i <= Math.Sqrt(n); i++)   {         // check if N is divisible by i,      // so that the other term in pair       // i.e. N/i is integral      if (n % i == 0)       {             // Check if i and N/i are coprime          if (__gcd(i, (n / i)) == 1)           {                 // Display the co- prime pairs              Console.WriteLine( "(" + i + ", " +                                 (n / i) + ")\n");              count++;          }      }  }     Console.WriteLine("\nNumber of coprime" +                       " pairs : " + count);  }     // Driver code  public static void Main ()  {      int N = 120;         countCoprimePairs(N);  }  }     // This code is contributed by Shashank

## PHP

 

Output:

The co- prime pairs are:
(3, 40)
(5, 24)
(8, 15)

Number of coprime pairs : 3


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