gcd() in Python

3

The Highest Common Factor (HCF) , also called gcd, can be computed in python using a single function offered by math module and hence can make tasks easier in many situations.

Naive Methods to compute gcd

  1. Using Recursion:

    # Python code to demonstrate naive
    # method to compute gcd ( recursion )
    
    def hcfnaive(a,b):
        if(b==0):
            return a
        else:
            return hcfnaive(b,a%b)
    
    a = 60
    b= 48
    
    # prints 12
    print ("The gcd of 60 and 48 is : ",end="")
    print (hcfnaive(60,48))
    

    Output:

    The gcd of 60 and 48 is : 12
    
  2. Using Loops

    # Python code to demonstrate naive
    # method to compute gcd ( Loops )
    
    
    def computeGCD(x, y):
    
        if x > y:
            small = y
        else:
            small = x
        for i in range(1, small+1):
            if((x % i == 0) and (y % i == 0)):
                gcd = i
                
        return gcd
    
    a = 60
    b= 48
    
    # prints 12
    print ("The gcd of 60 and 48 is : ",end="")
    print (computeGCD(60,48))
    

    Output:

    The gcd of 60 and 48 is : 12
    
  3. Using Euclidean Algorithm

    # Python code to demonstrate naive
    # method to compute gcd ( Euclidean algo )
    
    
    def computeGCD(x, y):
    
       while(y):
           x, y = y, x % y
    
       return x
    
    a = 60
    b= 48
    
    # prints 12
    print ("The gcd of 60 and 48 is : ",end="")
    print (computeGCD(60,48))
    

    Output:

    The gcd of 60 and 48 is : 12
    
  4. Using math.gcd() function of Python


    Using gcd() can compute the same gcd with just one line.

    math.gcd( x, y )
    Parameters : 
    x :  Non-negative integer whose gcd has to be computed.
    y : Non-negative integer whose gcd has to be computed.
    Return Value : 
    This method will return an absolute/positive integer value after 
    calculating the GCD of given parameters x and y.
    Exceptions : 
    When Both x and y are 0, function returns 0, If any number is a character ,
    Type error is raised.
    
    # Python code to demonstrate gcd()
    # method to compute gcd
    
    import math
    
    # prints 12
    print ("The gcd of 60 and 48 is : ",end="")
    print (math.gcd(60,48))
    

    Output:

    The gcd of 60 and 48 is : 12
    

    Common Exceptions


    Some common Exceptions in this function are :

    • Both numbers are 0, gcd is 0
    • If only either number is Not a number, Type Error is raised.
    # Python code to demonstrate gcd()
    # method exceptions
    
    import math
    
    # prints 0
    print ("The gcd of 0 and 0 is : ",end="")
    print (math.gcd(0,0))
    
    # Produces error
    print ("The gcd of a and 13 is : ",end="")
    print (math.gcd('a',13))
    

    Output:

    The gcd of 0 and 0 is : 0
    The gcd of a and 13 is : 
    

    Runtime Error :

    Traceback (most recent call last):
      File "/home/94493cdfb3c8509146254862d12bcc97.py", line 12, in 
        print (math.gcd('a',13))
    TypeError: 'str' object cannot be interpreted as an integer
    

    This article is contributed by Manjeet Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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