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GCD of Two Numbers

Certification: Basic Level Accuracy: 85.71% Submissions: 7 Points: 5

Write a C++ program that finds the Greatest Common Divisor (GCD) of two positive integers using the Euclidean algorithm.

Example 1
    

  • Input: a = 48, b = 18
    • 

  • Output: 6
    • 

  • Explanation: 
      

    • Step 1: Apply the Euclidean algorithm: gcd(a, b) = gcd(b, a % b) until b becomes 0.
      • 

    • Step 2: gcd(48, 18) = gcd(18, 48 % 18) = gcd(18, 12).
      • 

    • Step 3: gcd(18, 12) = gcd(12, 18 % 12) = gcd(12, 6).
      • 

    • Step 4: gcd(12, 6) = gcd(6, 12 % 6) = gcd(6, 0).
      • 

    • Step 5: When b becomes 0, the GCD is the value of a, which is 6.
      • 

    •
Example 2
    

  • Input: a = 13, b = 7
    • 

  • Output: 1
    • 

  • Explanation: 
      

    • Step 1: Apply the Euclidean algorithm: gcd(a, b) = gcd(b, a % b) until b becomes 0.
      • 

    • Step 2: gcd(13, 7) = gcd(7, 13 % 7) = gcd(7, 6).
      • 

    • Step 3: gcd(7, 6) = gcd(6, 7 % 6) = gcd(6, 1).
      • 

    • Step 4: gcd(6, 1) = gcd(1, 6 % 1) = gcd(1, 0).
      • 

    • Step 5: When b becomes 0, the GCD is the value of a, which is 1.
      • 

    •
Constraints
    

  • 1 ≤ a, b ≤ 10^9
    • 

  • Both inputs are positive integers
    • 

  • Time Complexity: O(log(min(a, b)))
    • 

  • Space Complexity: O(1)
    •
RecursionAlgorithmsHCL TechnologiesSwiggy
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Hint
Solution

Solution Hints

    
  
  • The Euclidean algorithm states that gcd(a, b) = gcd(b, a % b)
    • 
  
  • Use recursion or iteration to implement the algorithm
    • 
  
  • The base case is when the second number becomes 0, then the GCD is the first number
    •

Steps to solve by this approach:

 Step 1: Define a function find_gcd that takes two integers a and b.

 Step 2: Implement the Euclidean algorithm using a while loop that continues until b becomes 0.

 Step 3: In each iteration, set a temporary variable to b, update b to a % b, and update a to the temporary variable.

 Step 4: Return a, which will be the GCD when the loop terminates.

Submitted Code :