Python Program to Find Factorial of a Number

You can find the factorial of a number in Python using a loop like factorial = 1; for i in range(1, n+1): factorial *= i or using recursion with def factorial(n): return 1 if n == 0 else n * factorial(n-1).

Examples

Input0

Output1

Input5

Output120

Input1

Output1

How to Think About It

To find the factorial of a number, think of multiplying all whole numbers from 1 up to that number. For example, factorial of 5 means 1 × 2 × 3 × 4 × 5. You can do this by starting with 1 and multiplying by each number until you reach the input number.

Algorithm

1

Get the input number n

2

Start with a result variable set to 1

3

Multiply the result by each number from 1 to n

4

After the loop ends, return the result

Code

python

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

number = 5
print(f"Factorial of {number} is", factorial(number))

Output

Factorial of 5 is 120

Dry Run

Let's trace factorial(5) through the code

1

Initialize result

result = 1

2

Multiply by 1

result = 1 * 1 = 1

3

Multiply by 2

result = 1 * 2 = 2

4

Multiply by 3

result = 2 * 3 = 6

5

Multiply by 4

result = 6 * 4 = 24

6

Multiply by 5

result = 24 * 5 = 120

Iteration	Value of result
1	1
2	2
3	6
4	24
5	120

Why This Works

Step 1: Start with 1

We use result = 1 because multiplying by 1 does not change the value and it is the identity for multiplication.

Step 2: Multiply step by step

We multiply result by each number from 1 to n to build the factorial product.

Step 3: Return final result

After the loop finishes, result holds the factorial value, which we return.

Alternative Approaches

Recursion

python

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n - 1)

number = 5
print(f"Factorial of {number} is", factorial(number))

Uses function calling itself; elegant but can hit limits for very large n.

Using math module

python

import math
number = 5
print(f"Factorial of {number} is", math.factorial(number))

Simplest and fastest way using Python's built-in library.

Complexity: O(n) time, O(1) space

Time Complexity

The loop runs from 1 to n, so it takes O(n) time to compute the factorial.

Space Complexity

Only a few variables are used, so space is O(1), constant.

Which Approach is Fastest?

Using Python's built-in math.factorial() is fastest and most optimized, while recursion is elegant but slower and limited by recursion depth.

Approach	Time	Space	Best For
Loop	O(n)	O(1)	Simple and clear for beginners
Recursion	O(n)	O(n)	Elegant but limited by recursion depth
math.factorial()	O(n)	O(1)	Fastest and easiest for production