# Factorial Function in Python

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) = 1
Or,
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:-

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