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Find the GCD (Greatest Common Divisor) of Two Numbers

Certification: Basic Level Accuracy: 53.13% Submissions: 160 Points: 5

Write a Python program that finds the Greatest Common Divisor (GCD) of two positive integers.

Example 1
    

  • Input: a = 48, b = 18
    • 

  • Output: 6
    • 

  • Explanation: 

      

    • Step 1: Take two numbers a = 48 and b = 18 as input.
      • 

    • Step 2: Find factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
      • 

    • Step 3: Find factors of 18: 1, 2, 3, 6, 9, 18.
      • 

    • Step 4: Find the largest common factor: 6.
      • 

    • Step 5: Return 6 as the GCD.
      • 

    

    •
Example 2
    

  • Input: a = 17, b = 5
    • 

  • Output: 1
    • 

  • Explanation: 

      

    • Step 1: Take two numbers a = 17 and b = 5 as input.
      • 

    • Step 2: Find factors of 17: 1, 17.
      • 

    • Step 3: Find factors of 5: 1, 5.
      • 

    • Step 4: Find the largest common factor: 1.
      • 

    • Step 5: Return 1 as the GCD.
      • 

    

    •
Constraints
    

  • 1 ≤ a, b ≤ 10^9
    • 

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

  • Space Complexity: O(1)
    •
RecursionFacebookTCS (Tata Consultancy Services)
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Hint
Solution

Solution Hints

    
  
  • Use Euclidean algorithm: gcd(a, b) = gcd(b, a % b)
    • 
  
  • Recursive implementation: if b == 0, return a; else return gcd(b, a % b)
    • 
  
  • Iterative implementation: while b != 0: a, b = b, a % b; return a
    •

The following are the steps to find the GCD of two numbers:

  • Define the function gcd(a, b).

  • Use a while loop to apply the Euclidean algorithm: a, b = b, a % b.

  • Return a when b becomes 0.

  • Call the function and print the result.

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