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++ 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;
} |
// 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 |
# 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 |
// 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 |
<script> // javascript implementation to print any pair of integers // whose summation of GCD and LCM is equal to integer N // Function to print the required pair function printPair(n)
{
// Print the pair
document.write(1 + " " + (n - 1));
}
// Driver code
var n = 14;
printPair(n);
// This code is contributed by aashish1995 </script> |
1 13
Time Complexity:O(1)
Auxiliary Space:O(1)