Print any pair of integers with sum of GCD and LCM equals to N

Given an integer N, the task is to print any pair of integers that have the sum of GCD and LCM equal to N.

Examples:

Input: N = 14
Output: 1, 13
Explanation:
For the given pair we have GCD(1, 13) = 1 and LCM (1, 13) = 13. Sum of GCD and LCM = 1 + 13 = 14.

Input: 2
Output: 1 1
Explanation:
For the given pair we have GCD(1, 1) = 1 and LCM (1, 1) = 1. Sum of GCD and LCM = 1 + 1 = 2.

Approach:



To solve the problem mentioned above let us consider the pair to be (1, n-1). GCD of (1, n-1) = 1 and LCM of (1, n-1) = n – 1. So the sum of GCD and LCM = 1 + (n – 1) = n. Hence the pair (1, n – 1) will be the pair which has the sum of GCD and LCM equal to N.

Below is the implementation of the above approach:

C++

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// C++ implementation to Print any pair of integers
// whose summation of GCD and LCM is equal to integer N
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to print the required pair
void printPair(int n)
{
    // print the pair
    cout << 1 << " " << n - 1;
}
  
// Driver code
int main()
{
    int n = 14;
  
    printPair(n);
  
    return 0;
}

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Java

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// Java implementation to print any pair of integers
// whose summation of GCD and LCM is equal to integer N
class GFG{
  
// Function to print the required pair
static void printPair(int n)
{
    // Print the pair
    System.out.print(1 + " " + (n - 1));
}
  
// Driver code
public static void main(String[] args)
{
    int n = 14;
    printPair(n);
}
}
  
// This code is contributed by gauravrajput1

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Python3

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# Python3 implementation to print any 
# pair of integers whose summation of
# GCD and LCM is equal to integer N 
  
# Function to print the required pair 
def printPair(n): 
  
    # Print the pair 
    print("1", end = " ")
    print(n - 1)
  
# Driver code 
n = 14
printPair(n)
  
# This code is contributed by PratikBasu

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C#

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// C# implementation to print any pair
// of integers whose summation of
// GCD and LCM is equal to integer N
using System;
  
public class GFG{
  
// Function to print the required pair
static void printPair(int n)
{
      
    // Print the pair
    Console.Write(1 + " " + (n - 1));
}
  
// Driver code
public static void Main(String[] args)
{
    int n = 14;
    printPair(n);
}
}
  
// This code is contributed by Princi Singh

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Output:

1 13

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