gcd() in Python

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.

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
   

   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
   

   
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