The math.gcd() function in Python is used to compute the greatest common divisor (GCD) of two or more integers. The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. This function is particularly useful in number theory and various mathematical applications.

Syntax

import math
result = math.gcd(a, b)

• a: The first integer.
• b: The second integer.

Return Value

• Returns the greatest common divisor of a and b, which is of type int.
• If either a or b is zero, the function returns the absolute value of the non-zero argument.

Examples

1. Calculating the GCD of two positive integers:

   import math
   
   result = math.gcd(48, 18)
   print(result)  # Output: 6 (because 6 is the largest number that divides both 48 and 18)
   

2. Calculating the GCD with one negative integer: The GCD function considers only the absolute values of the arguments.

   result = math.gcd(-48, 18)
   print(result)  # Output: 6
   

3. Calculating the GCD with zero: If one of the numbers is zero, the GCD is the absolute value of the other number.

   result = math.gcd(0, 5)
   print(result)  # Output: 5
   result = math.gcd(5, 0)
   print(result)  # Output: 5
   

4. Using math.gcd() with large numbers:

   result = math.gcd(123456, 789012)
   print(result)  # Output: 12
   

5. Calculating the GCD of multiple integers: To find the GCD of more than two integers, you can use functools.reduce() along with math.gcd():

   from functools import reduce
   
   numbers = [48, 64, 80]
   result = reduce(math.gcd, numbers)
   print(result)  # Output: 16
   

Summary

• The math.gcd() function computes the greatest common divisor of two integers.
• It returns an integer that represents the GCD, considering only the absolute values of the inputs.
• The function handles zero gracefully, returning the absolute value of the non-zero argument when one of the numbers is zero.
• This function is useful in various mathematical contexts, such as simplifying fractions, finding common denominators, and solving problems in number theory.The math.gcd() function in Python is used to compute the greatest common divisor (GCD) of two or more integers. The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder