Python uses the divide-and-conquer method for computing factorials.
See if this helps.
Answer from esskayesss on Stack OverflowGeeksforGeeks
geeksforgeeks.org › python-math-factorial-function
Python | math.factorial() function - GeeksforGeeks
February 16, 2023 - In Python, math module contains ... a numeric expression. Returns: factorial of desired number. Time Complexity: O(n) where n is the input number....
Reddit
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r/learnpython on Reddit: Maths factorial Function
December 29, 2023 -
I’m curious if anyone can explain the speed of math.factorial() compared to the typical ways you’d see someone write it on their own (iterative, recursive, ect). What makes it so much faster and how is it working under the hood?
Thanks in advance.
Top answer 1 of 2
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It's implemented in native code, and it does some clever tricks on top of that: https://github.com/python/cpython/blob/f46987b8281148503568516c29a4a04a75aaba8d/Modules/mathmodule.c#L2013
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A helpful tool for me to look at how to calculate time and space complexity is https://www.bigocalc.com/ It will explain WHY the function has "X" time complexity. for math.factorial() it says... import math math.factorial(1000) The time complexity of calculating the factorial of 1000 using the math.factorial() function is O(n), where n is the input number. This is because the function iterates from 1 to n, multiplying each number along the way. In this case, n is 1000, so the function will perform 1000 multiplications. The space complexity is O(1) because the function does not use any additional space that grows with the input size. It only requires a constant amount of space to store the result. for this defined function it says... def factorial(num): product = 1 while num > 0: product *= num num -= 1 return product The time complexity of this function is O(n), where n is the input number. This is because the function uses a while loop that iterates n times, multiplying the product by num in each iteration. The space complexity of this function is O(1), constant space. This is because the function only uses a single variable, product, to store the result and does not create any additional data structures that grow with the input size. Then for a recursive function... def factorail_recur(num): return num * factorial(num - 1) factorial(1000) The time complexity of this function is O(n), where n is the value of the input num. This is because the function calls itself recursively n times, each time reducing the value of num by 1. The space complexity of this function is O(n) as well, because each recursive call adds a new frame to the call stack, and the maximum depth of the call stack is equal to the value of num. Therefore, the space required by the call stack grows linearly with the value of num.
Unstop
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Factorial Program In Python | Examples & Complexity Analysis
February 4, 2025 - Here is a detailed complexity analysis of the different methods used to write a factorial program in Python programming language: Factorial of a number is the product of all preceding integers and the respective number itself. There are many ways to write a factorial program in Python, including iterative loops, recursive functions, and built-in functions like math.factorial() and numpy.prod().
GeeksforGeeks
geeksforgeeks.org › python › factorial-in-python
factorial() in Python - GeeksforGeeks
The factorial of a number n (written as n!) is the product of all positive integers from 1 to n. ... Python provides a function math.factorial() that computes factorial without writing the entire loop manually.
Published December 18, 2025
SSRN
papers.ssrn.com › sol3 › Delivery.cfm › SSRN_ID4586398_code5814333.pdf
A Review of Factorial Algorithms and their Efficient ...
October 26, 2023 - This paper elaborates on the implementations of all scenarios in a manner that comprehensively addresses both the temporal complexity and memory constraints, particularly when dealing with substantial sample values. Keywords: factorial algorithms, big data, AI and ML, GPU accelerated computing, Python, data science
PrepBytes
prepbytes.com › home › python › factorial function in python
Factorial Function in Python
February 25, 2023 - This function takes a single argument, which is the number whose factorial is to be calculated and returns the factorial of that number. The time complexity of the factorial() function is O(n), where n is the input integer.
Python
bugs.python.org › issue8692
Issue 8692: Use divide-and-conquer for faster factorials - Python tracker
This issue tracker has been migrated to GitHub, and is currently read-only. For more information, see the GitHub FAQs in the Python's Developer Guide · This issue has been migrated to GitHub: https://github.com/python/cpython/issues/52938
Sanfoundry
sanfoundry.com › python-program-find-factorial-number-recursion
Factorial Program in Python - Sanfoundry
October 10, 2023 - Time Complexity: O(n) The time complexity of the above code is O(n) because the while loop iterates n times, where n is the input number. 📌 Limited Seats! Register Now - Free AI-ML Certification (February 2026) Space Complexity: O(1) The space ...
Medium
medium.com › @fammimanahil › understanding-the-factorial-function-in-python-a-complete-guide-1cb2f9b50d14
Understanding the Factorial Function in Python: A Complete Guide | by Fatima Zaheer | Medium
December 30, 2024 - Here’s an example using recursion: def factorial_recursive(n): if n == 0 or n == 1: return 1 else: return n * factorial_recursive(n - 1) Answer: The time complexity is , where is the input number.
Pickl
pickl.ai › home › python programming › program to find the factorial of a number in python
Program to Find the Factorial of a Number in Python
February 20, 2025 - Recursive Approach: Calls itself n times, also resulting in O(n) time complexity. However, recursive function calls add extra overhead, slowing down execution. Built-in Function (math.factorial()): Python’s built-in method is highly optimised, ...
Jaro Education
jaroeducation.com › home › blog › factorial program in python explained with examples
Different Approaches to Compute Factorial Program in Python
April 17, 2025 - So, iteration and recursion are completely different approaches in Python. Also, the computing code for factorial in Python is different for each approach. The time complexity of a recursive factorial program in Python is O(n).
Sololearn
sololearn.com › en › Discuss › 1479542 › program-for-factorial-with-time-complexity-less-than-on
program for factorial with time complexity less than o(n) | Sololearn: Learn to code for FREE!
August 31, 2018 - The function fact(n) itself has a time complexity of O(1). I don't think it's possible without this kind of cheating. https://code.sololearn.com/cnHlSF13axhB/?ref=app ... How about extracting all the 2's from factorial? For example, factorial(12) = 2^10 * (1) * (1 * 3) * (1 * 3 * 5) * (1 * 3 * 5 * 7 * 9 * 11) Each term in parentheses can be used to help find the next term.
InterviewBit
interviewbit.com › courses › programming › time-complexity
Time Complexity - InterviewBit
Later you would see that the time complexity of the first way is O(n) and that of the second way is O(logn).
Quora
quora.com › I-have-an-algorithm-with-factorial-time-complexity-What-are-the-ways-to-find-algorithm-which-will-approximate-the-result-and-work-faster
I have an algorithm with factorial time complexity. What are the ways to find algorithm which will approximate the result and work faster? - Quora
Answer (1 of 2): There is no technical way to answer this question without knowing what the problem you are studying exactly is and what the algorithm even looks like. Your algorithm for solving a problem might be considerably slower than possibly the best-known algorithm, or it might indeed be t...
Unstop
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How To Find Factorial Of A Number Using Recursion In Python? // Unstop
November 8, 2024 - Finding the factorial of a number using recursion is a powerful example of how recursion can simplify complex mathematical calculations. By breaking the problem down into smaller, repetitive steps, recursion enables us to compute factorials with clean and concise code.
Wikipedia
en.wikipedia.org › wiki › Factorial
Factorial - Wikipedia
1 week ago - Although directly computing large factorials using the product formula or recurrence is not efficient, faster algorithms are known, matching to within a constant factor the time for fast multiplication algorithms for numbers with the same number of digits. The concept of factorials has arisen independently in many cultures: In Indian mathematics, one of the earliest known descriptions of factorials comes from the Anuyogadvāra-sūtra, one of the canonical works of Jain literature, which has been assigned dates varying from 300 BCE to 400 CE.
Facebook
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Which algorithm is faster, custom factorial or math. ...
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Quora
quora.com › How-do-I-find-factorial-of-a-number-in-O-logn-time-complexity
How to find factorial of a number in O(logn) time complexity - Quora
Answer (1 of 5): If you want to find the exact factorial, I would say it is impossible because n! will have O(n) digits. Printing/Storing the output will take O(n). If you’re happy with an approximate value, you can use Stirling's approximation.
PYnative
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Python Basic Exercise for Beginners: 40 Coding Problems with Solutions
1 month ago - Use Online Python Code Editor to solve exercises. Let us know if you have any alternative solutions in the comments section below. This will help other developers. ... Exercise 1. Arithmetic Product and Conditional Logic · Exercise 2. Cumulative Sum of a Range · Exercise 3. String Indexing and Even Slicing · Exercise 4. String Slicing and Substring Removal · Exercise 5. Variable Swapping (The In-Place Method) Exercise 6. Calculating Factorial with a Loop