The Python Factorial Function Explained

The Python factorial function is a very useful tool. In this blog, I will explain what the Python factorial function is and show you how to write it.

What is the Python Factorial Function?

The Python factorial function, denoted by ! and called factorial, requires that you pass in a number. The factorial function will return the product of all numbers from our chosen number down to 1.

The Python factorial function is one of the Math Functions in the Python math library. The factorial function is represented by an exclamation point. e.g. 3! = 3 * 2 * 1 = 6

In mathematics, the factorial of a number is the product of all positive integers less than or equal to that number. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120

The factorial of zero (0!) is defined as being 1, and 0! = 1

Factorials are used in various areas of mathematics, but mostly in Combinatorics, where it gives the number of ways k objects can be arranged into an ordered sequence.

The Python Factorial Function Syntax

The Python factorial function is one of the most widely used functions in mathematics. It is defined as the product of all positive integers from 1 to a given number n. In other words, it is the sum of all numbers from 0 to n, where n is non-negative.

The mathematical notation for factorial is:


The exclamation point after n in the equation above means factorial. For example, 5! = 1 x 2 x 3 x 4 x 5 = 120. Also written as 5! = 120. The Python factorial function helps to do this very easily.

It can be observed that:

1! = 1

2! = 2 x 1 = 2

3! = 3 x 2 x 1 = 6

4! = 4 x 3 x 2 x 1 = 24

5! = 5 x 4 x 3 x 2 x 1 = 120

The factorial is a basic mathematical function often used when solving combination and permutation problems in mathematics and probability. The factorial of a number, n, is the product of all integers from 1 to n. For example, the factorial of 5 (denoted as 5!) is 5*4*3*2*1 = 120. As you can see, if you have a larger number like 5, the factorial can become very large, very quickly.

If your math is rusty or non-existent (like mine), it’s easy to make mistakes when writing the factorial function in Python. So let’s go over some of the basics so that we’re all on the same page before diving into our code example.

The Recursive Factorial Function

The factorial function can be calculated using a recursive approach where the function calls itself until it reaches one or a base case. You should be familiar with recursive functions since they are often used to solve many different types of problems. As an example, here is what the pseudo-code looks like for calculating a factorial:


IF n == 1 THEN RETURN 1;

The factorial function is a mathematical function that multiplies a given number, called the argument, by all of the positive integers smaller than it. You can write out the factorial function as an exclamation point: x! = x * (x – 1) * (x – 2) * (x – 3) … 3 * 2 * 1

This is useful because you can use it to calculate the number of different ways you can arrange a set of objects of size x. For example, if you have three distinct objects, there are six different ways you can arrange them (3 objects x 2 objects x 1 object).

To program this in Python, we need to do some calculation. The first thing we’ll do is define our function: def factorial(x):

Next, we need to make sure that whatever number gets passed into our function is actually a positive integer. Otherwise, things will break. We’ll use an if statement and raise an error if the argument isn’t an integer: def factorial(x):

if type(x) != int or x < 0: raise ValueError("factorial() only accepts positive ints") Now that we've checked that our argument is valid, we'll use another if The factorial function is a mathematical function that multiplies a given number, by every number below it. For example: 4! = 4 × 3 × 2 × 1 = 24 5! = 5 × 4 × 3 × 2 × 1 = 120 The factorial of a negative number doesn't exist, so the factorial of -1 can't be defined. It is only defined for positive integers. The factorial is an important mathematical function and there are many ways to calculate it in Python. Here I will explain the most used methods. The factorial function is a built-in function in Python that is used to find the factorial of a number. A factorial of a number can be calculated by multiplying the number with all the positive integers less than or equal to it. The value of 0! (factorial 0) is 1, denoted as 0! = 1. A factorial program in Python is written as follows: def factorial(n): if n == 0: return 1 else: return n * factorial(n-1)

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