Factorial function in python | In this program, we will discuss how to find the factorial of a number using a function in python. Also, discuss how to find the factorial of a number using math.factorial() function.

Factorial of a positive integer number specifies a product of all integers from 1 to that number. It is defined by the symbol exclamation mark (!).

**General case** for finding factorial

**factorial(n) = n * factorial(n-1)**

The **base case** for finding factorial

**factorial(0) = 1Or,factorial(1) = 1**

Factorial (n) = 1 * 2 * … * (n-1) * n

Or, n * (n-1) * … * 2 * 1

The factorial of a negative number and float number doesn’t exist. The value of 0! is 1, according to the convention for an empty product.

The factorial of 6 is denoted as 6! = 1*2*3*4*5*6 or 6*5*4*3* 2*1

We can write 6! as,

6! = 6 * 5!

Similarly, we can write

5! = 5 * 4!

4! = 4 * 3!

3! = 3 * 2!

2! = 2 * 1!

1! = 1 * 0!

0! = 1

## Factorial Program in Python using Function

In this program, We can also take the help of a user-defined function. A function is a block of code that performs a specific task.

```
# Python program to find the factorial of a number using function
def factorial(num): #user-defined function
# find factorial of a number
fact = 1
for i in range(1,num + 1):
fact = fact*i
return fact
# take input
num = int(input("Enter number: "))
# check number is positive, negative, or zero
if num < 0:
print('Factorial does not exist for negative numbers')
elif num == 0:
print('The factorial of 0 is 1')
else:
# calling function
print('The factorial of',num,'is',factorial(num))
```

Output for the different input values:-

Enter number: 4

The factorial of 4 is 24

Enter number: -4

Factorial does not exist for negative numbers

Enter number: 6

The factorial of 6 is 720

In this program, we will be the first defined function.

```
def factorial(num): #user-defined function
# find factorial of a number
fact = 1
for i in range(1,num + 1):
fact = fact*i
return fact
```

Inputs are scanned using the input() function and stored in variable num.

`num = int(input("Enter number: "))`

Check number is positive, negative, or zero. Factorial is not defined for negative numbers and the factorial of zero is one, 0! = 1. The number is positive then it passed to the factorial() function to compute the factorial of the number and the result will be displayed on the screen.

```
if num < 0:
print('Factorial does not exist for negative numbers')
elif num == 0:
print('The factorial of 0 is 1')
else:
# calling function
print('The factorial of',num,'is',factorial(num))
```

## Program using Math Function

In the Math module of Python, the factorial() function is already available, which calculates the factorial of the given number and returns the result. See more:- Math.factorial() in Python.

In this program, we will find the factorial of a number using math.factorial() function. The factorial() function will be imported from the math file.

```
# Python program to find the factorial of a number using math function
import math #math module
def factorial(num):
# find factorial of a number
print('The factorial of',num,'is', math.factorial(num))
# take input
num = int(input("Enter number: "))
# calling function
factorial(num)
```

Output for the different input values:-

Enter number: 3

The factorial of 3 is 6

Enter number: 0

The factorial of 0 is 1

Enter number: -6

Traceback (most recent call last):

File “main.py”, line 13, in

factorial(num)

File “main.py”, line 7, in factorial

print(‘The factorial of’,num,’is’, math.factorial(num))

ValueError: factorial() not defined for negative values

Enter number: 3.5

Traceback (most recent call last):

File “main.py”, line 10, in

num = int(input(“Enter number: “))

ValueError: invalid literal for int() with base 10: ‘3.5’

In the above program, find the factorial of a number in python using for loop and while loop but many different ways to find factorial of a number in python.

Similar Program to find factorial in Python:-

- Python program to find factorial using recursion
- Python program to find factorial using math.factorial()
- Program to find factorial using for loop and while loop

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