The math.factorial() function in Python is used to compute the factorial of a non-negative integer. The factorial of a number $n$ (denoted as $n!$) is the product of all positive integers from 1 to $n$. By definition, the factorial of 0 is 1.

Syntax

import math
result = math.factorial(n)

• n: A non-negative integer for which you want to compute the factorial.

Return Value

• Returns the factorial of n, which is of type int.
• Raises a ValueError if n is a negative integer.

Examples

1. Calculating the factorial of a positive integer:

   import math
   
   result = math.factorial(5)
   print(result)  # Output: 120 (because 5! = 5 × 4 × 3 × 2 × 1)
   

2. Calculating the factorial of zero: The factorial of 0 is defined as 1.

   result = math.factorial(0)
   print(result)  # Output: 1
   

3. Calculating the factorial of a larger number:

   result = math.factorial(10)
   print(result)  # Output: 3628800 (because 10! = 10 × 9 × 8 × ... × 1)
   

4. Handling negative integers: Attempting to calculate the factorial of a negative integer will raise a ValueError.

   try:
       result = math.factorial(-3)
   except ValueError as e:
       print(e)  # Output: factorial() not defined for negative values
   

Summary

• The math.factorial() function computes the factorial of a non-negative integer.
• It returns an integer representing the factorial value.
• The function handles the case of zero by returning 1.
• An error is raised for negative integers, making it a robust choice for calculating factorials. This function is particularly useful in combinatorics, probability, and various mathematical computations.