Given two integers A and B, the task is to find two co-prime numbers C1 and C2 such that C1 divides A and C2 divides B.
Examples:
Input: A = 12, B = 16
Output: 3 4
12 % 3 = 0
16 % 4 = 0
gcd(3, 4) = 1Input: A = 542, B = 762
Output: 271 381
Naive approach: A simple solution is to store all of the divisors of A and B then iterate over all the divisors of A and B pairwise to find the pair of elements which are co-prime.
Efficient approach: If an integer d divides gcd(a, b) then gcd(a / d, b / d) = gcd(a, b) / d. More formally, if num = gcd(a, b) then gcd(a / num, b / num) = 1 i.e. (a / num) and (b / num) are relatively co-prime.
So in order to find the required numbers, find gcd(a, b) and store it in a variable gcd. Now the required numbers will be (a / gcd) and (b / gcd).
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to find the required numbers void findNumbers(int a, int b) { // GCD of the given numbers int gcd = __gcd(a, b); // Printing the requried numbers cout << (a / gcd) << " " << (b / gcd); } // Driver code int main() { int a = 12, b = 16; findNumbers(a, b); return 0; } |
Java
// Java implementation of the approach import java.math.*; class GFG { public static int findGCD(int a, int b) { if(b == 0) return a; else return findGCD(b, a % b); } // Function to find the required numbers static void findNumbers(int a, int b) { // GCD of the given numbers int gcd = findGCD(a, b); // Printing the requried numbers System.out.println((a / gcd) + " " + (b / gcd)); } // Driver code public static void main(String[] args) { int a = 12, b = 16; findNumbers(a, b); } } // This code is contributed by Naman_Garg |
Python3
# Python3 implementation of the approach # import gcd function from math module from math import gcd # Function to find the required numbers def findNumbers(a, b) : # GCD of the given numbers __gcd = gcd(a, b); # Printing the requried numbers print((a // __gcd), (b // __gcd)); # Driver code if __name__ == "__main__" : a = 12; b = 16; findNumbers(a, b); # This code is contributed by AnkitRai01 |
C#
// C# implementation of the approach using System; class GFG { public static int findGCD(int a, int b) { if(b == 0) return a; else return findGCD(b, a % b); } // Function to find the required numbers static void findNumbers(int a, int b) { // GCD of the given numbers int gcd = findGCD(a, b); // Printing the requried numbers Console.Write((a / gcd) + " " + (b / gcd)); } // Driver code static public void Main () { int a = 12, b = 16; findNumbers(a, b); } } // This code is contributed by ajit |
3 4
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