Let’s understand the different ways to write a Python program to calculate factorial of a number.
What is factorial of a number?
The factorial of a given number (N) is defined as the product obtained by multiplying all the numbers between the given number (N) and 1. For example, the factorial of 5 is the result of the expression 5x4x3x2x1, which is equal to the value 120. Similarly, the factorial of 6 is the result of the expression 6x5x4x3x2x1, which is equal to the value 720. Some important observations.
- The factorial of number 2 is the value 2 (2! = 2)
- The factorial of number 1 is the value 1 (1! = 1)
- The factorial of number 0 is the value 1 (0! = 1)
- The factorial of negative numbers is not defined
- Factorial can also be calculated recursively using the definition n!=n*(n-1)!
How to calculate the factorial of a number?
To calculate the factorial of a given number (N), we create a loop which starts with 1 and iterates till the given number N. The factorial value is initialised to 1 before the loop starts. During each iteration, the loop index number is multiplied with the factorial value. As the loop ends, the factorial contains the product of all numbers between 1 and N.
Python Code (to calculate factorial of a number)
#code to calculate factorial
n = int(input("Enter a number "))
f = 1
i = 1
while i<=n:
f=f*i
i=i+1
print("The factorial is", f)Python Code (to calculate factorial using functions)
The code to calculate factorial of a number can be written using a function. The function takes the number as an arguments and returns the factorial of the number as the result.
#function to calculate factorial
def factorial(n):
f=1
i=1
while i<=n:
f=f*i
i=i+1
return f
#code to test the above function
n = int(input("Enter a number "))
print("The factorial is", factorial(n))
Python Code (to calculate factorial using recursion)
The function to calculate factorial of a number can be written using recursion, where the function calls itself to calculate the result. Observe that the recursive function does not need a loop to calculate the result, as the recursive function itself behaves like an implicit loop.
#recursive function to calculate factorial
def factorial(n):
if n==0:
return 1
else:
return n*factorial(n-1)
#code to test the above function
n = int(input("Enter a number "))
print("The factorial is", factorial(n))