Python Program to Find the Factorial of a Number

Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n in Python. 

Example

Simple Python program to find the factorial of a number

# Input: An integer number
num = 6

# Initialize the factorial variable to 1
factorial = 1

# Calculate the factorial using a for loop
for i in range(1, num + 1):
    factorial *= i

# Output: The factorial of the number
print(f"The factorial of {num} is {factorial}")

Output

The factorial of 6 is 720

Get Factorial of a Number using a Recursive Approach

This Python program uses a recursive function to calculate the factorial of a given number. The factorial is computed by multiplying the number with the factorial of its preceding number.

# Python 3 program to find 
# factorial of given number
def factorial(n):
    
    # single line to find factorial
    return 1 if (n==1 or n==0) else n * factorial(n - 1) 

# Driver Code
num = 5
print("Factorial of",num,"is",factorial(num))

Output:

Factorial of 5 is 120

Time Complexity: O(n)
Auxiliary Space: O(n)

Find Factorials quickly using One liner (Using Ternary Operator)

This Python function calculates the factorial of a number using recursion. It returns 1 if n is 0 or 1; otherwise, it multiplies n by the factorial of n-1.

def factorial(n):

    # single line to find factorial
    return 1 if (n==1 or n==0) else n * factorial(n - 1) 


# Driver Code
num = 5
print ("Factorial of",num,"is",
      factorial(num))

Output:

Factorial of 5 is 120

Time Complexity: O(n)
Auxiliary Space: O(n)

Factorial Function in Maths

In Python, math module contains a number of mathematical operations, which can be performed with ease using the module. math.factorial() function returns the factorial of desired number.

# Python 3 program to find
# factorial of given number
import math

def factorial(n):
    return(math.factorial(n))


# Driver Code
num = 5
print("Factorial of", num, "is",
      factorial(num))

# This code is contributed by Ashutosh Pandit

Output:

Factorial of 5 is 120

Time complexity: O(N)
Auxiliary space: O(1)

Find the Factorial of a Number Using NumPy

This Python code calculates the factorial of n using NumPy. It creates a list of numbers from 1 to n, computes their product with numpy.prod(), and prints the result.

import numpy
n=5
x=numpy.prod([i for i in range(1,n+1)])
print(x)

Output 

120

Time Complexity: O(n)
Auxiliary Space: O(1)

Prime Factorization Method to find Factorial

1. Initialize the factorial variable to 1.
2. For each number i from 2 to n, do the following:
   a. Find the prime factorization of i.
   b. For each prime factor p and its corresponding power k in the factorization of i, multiply the factorial variable by p raised to the power of k.
3. Return the factorial variable.

# Function to find prime factors of a number
def primeFactors(n):
    factors = {}
    i = 2
    while i*i <= n:
        while n % i == 0:
            if i not in factors:
                factors[i] = 0
            factors[i] += 1
            n //= i
        i += 1
    if n > 1:
        if n not in factors:
            factors[n] = 0
        factors[n] += 1
    return factors

# Function to find factorial of a number
def factorial(n):
    result = 1
    for i in range(2, n+1):
        factors = primeFactors(i)
        for p in factors:
            result *= p ** factors[p]
    return result

# Driver Code
num = 5
print("Factorial of", num, "is", factorial(num))

Factorial of 5 is 120

Time Complexity: O(sqrt(n))
Auxiliary Space: O(sqrt(n))

Please refer complete article on Program for factorial of a number for more details!

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• factorial

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