**Calculating the Factorial of a Number**

**Approach 1- Using Recursion**

Recursion is one of the most common ways to calculate Python factorial. Recursion is a programming technique in which a function calls itself repeatedly until the specified condition is met. Here is an example of how to find out the factorial of a number using recursion in Python.

**Code in Python**

```
def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
print("Factorial of 7 =", factorial(7))
```

**Output**

`Factorial of 7 = 5040`

In this code, the `factorial` function takes an integer `n` as input and returns the product of all positive integers up to `n`. The base case of the recursion is when `n` is equal to 0, in which case the function returns 1. Otherwise, the function multiplies `n` by the result of calling `factorial(n-1)`.

**Approach 2- Using a Loop**

Another way to calculate Python factorial is by using a loop. Here is an example of how to find out the factorial of a number using a loop in Python.

**Code in Python**

```
def factorial(n):
result = 1
for i in range(1, n+1):
result *= i
return result
```

**Output**

`Factorial of 6 = 720`

In this code, the `factorial` function takes an integer `n` as input and returns the product of all positive integers up to `n`. The function initializes a variable `result` to 1, and then uses a `for` loop to multiply `result` by each integer from 1 to `n`.

**Approach 3-Using the Python module**

The Factorial of a number can also be calculated using the Python method, math.factorial(). Here is how to

**Syntax**

Here is the syntax of this function after importing the math library in python:

`math.factorial(x)`

**Parameters**

x = the number you want to find the factorial of.

**Return Value**

The factorial of the number entered.

**Errors and exceptions**

**ValueError** - This factorial method only works for positive integers and gives an error if used with negative integers.

## Examples

### Code in Python - Factorial of a positive number

```
import math
print("Factorial of 5 = :" ,math.factorial(5))
```

**Output**

`Factorial of 5 = : 120`

### Code in Python - Factorial of a Negative Number

```
import math
print("Factorial of -5 = :" ,math.factorial(-5))
```

**Output**

Now that we have seen the ways of finding Python factorial, we will look at some frequently asked questions on the same.

Also see, __Convert String to List Python__

**Frequently Asked Questions**

**What is the largest factorial that can be calculated in Python?**

The largest factorial that can be calculated in Python is limited by the maximum size of an integer in Python. In most implementations, this is 2^31-1 or 2^63-1, depending on whether the implementation is 32-bit or 64-bit.

**What is the time complexity of calculating factorial using recursion?**

The time complexity of calculating factorial using recursion is O(n), where n is the input number. This is because the recursion involves n function calls, each taking O(1) time.

**What is the time complexity of calculating factorial using a loop?**

The time complexity of calculating factorial using a loop is also O(n), where n is the input number. This is because the loop involves n iterations, each taking O(1) time.

**Conclusion**

In this article, we explored three ways to calculate Python factorial: recursion, a loop, and the function in Python. The first two methods have a time complexity of O(n) and can be used to calculate the factorial of any positive integer.

The choice between these methods depends on personal preference and the application's specific requirements. Factorials are an essential mathematical concept widely used in various fields, and Python provides several ways to calculate them efficiently.

Try to solve the __Factorial of a Number__ problem to practice what you learned!

Check out __python Factorial of a Number__ for the solution.

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