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Calculate Factorial Recursively

Published at19 Apr 2026
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This problem introduces a classic recursive idea. You are given one non-negative integer n, and your task is to calculate n!, which is called the factorial of n.

Factorial means multiplying all positive integers from 1 up to n. For example, 5! means 5 * 4 * 3 * 2 * 1, so the answer is 120. By definition, 0! is 1.

This problem is a natural fit for recursion because factorial can be defined in terms of a smaller factorial:

factorial(n) = 1, if n = 0 factorial(n) = n * factorial(n - 1), if n > 0

So the task is to read n, compute its factorial with a recursive function, and print the result.

Example Input & Output

Example 1
Input
n = 5
Output
120
Explanation

5 * 4 * 3 * 2 * 1 = 120.

Example 2
Input
n = 4
Output
24
Explanation

4 * 3 * 2 * 1 = 24.

Example 3
Input
n = 0
Output
1
Explanation

By definition, 0! = 1.

Algorithm Flow

Recommendation Algorithm Flow for Calculate Factorial Recursively
Recommendation Algorithm Flow for Calculate Factorial Recursively

Solution Approach

A recursive solution works by breaking the problem into a smaller version of itself.

The most important part is the base case. If n = 0, the factorial is already known, which is 1. This stops the recursion.

For any value greater than 0, use the recursive rule:

return n * factorial(n - 1)

That means if you want factorial(4), you calculate 4 * factorial(3). Then factorial(3) becomes 3 * factorial(2), and so on, until the call reaches factorial(0).

Once the base case returns 1, the calls finish in reverse order and build the final answer. For example, factorial(4) becomes 4 * 3 * 2 * 1 * 1 = 24.

The full algorithm is: read n, call a recursive function such as factorial(n), and print the result. The recursion depth is n, so the running time is O(n).

Best Answers

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