Factorial of a Number in C, C++, Java & Python – Code with Explanation & Examples in Short and Simple

C Program

#include<stdio.h>

int f(int n) {
    return n < 2 ? 1 : n * f(n - 1);
}

int main() {
    int n;
    scanf("%d", &n);
    printf("%d", f(n));
}

C Output

Input: 5  
Output: 120

C++ Program

#include<iostream>
using namespace std;

int f(int n) {
    return n < 2 ? 1 : n * f(n - 1);
}

int main() {
    int n;
    cin >> n;
    cout << f(n);
}

C++ Output

Input: 5  
Output: 120

JAVA Program

import java.util.*;

class F {
    static int f(int n) {
        return n < 2 ? 1 : n * f(n - 1);
    }

    public static void main(String[] args) {
        int n = new Scanner(System.in).nextInt();
        System.out.print(f(n));
    }
}

JAVA Output

Input: 5  
Output: 120

Python Program

def f(n):
    return 1 if n < 2 else n * f(n - 1)

print(f(int(input())))

Python Output

Input: 5  
Output: 120

In-Depth Learning – Whole Concept in Paragraphs

What Is a Factorial?

The factorial of an integer n (n!) is the product of all the positive integers up to and including n. Algebraically, it's represented as n! = n × (n-1) × (n-2) ×. × 1. For instance, 5! = 5 × 4 × 3 × 2 × 1 = 120. It is a fundamental idea in mathematics, particularly in permutations, combinations, probability, and algebra. In programming, factorial is also used to introduce recursion and loop-based calculations, since it is an easy problem with a naturally cyclical nature.

Why Use Recursion for Factorial?

The recursive method of factorial is perfect since factorial is actually defined recursively: n! = n × (n-1)!. Thus, when you create a function that returns n * factorial(n-1), you're creating code that mirrors the math formula. The recursive answer is elegant and simple and a great way to get students used to functions calling themselves with a reducing value until a terminating condition is reached.

Example

Let's say we want to compute the factorial of 5. The function begins with f(5) = 5 × f(4). But to compute f(4), we need to compute f(3), then f(2), and lastly f(1). At that moment, the function reaches the base case where n < 2 and returns 1. Then the recursive stack starts to unroll:

f(1) = 1

f(2) = 2 × 1 = 2

f(3) = 3 × 2 = 6

f(4) = 4 × 6 = 24

f(5) = 5 × 24 = 120

This recursive unwinding makes it easier to see how the problem is reduced and rebuilt stepwise.

Real-Life Analogy

Suppose you are piling chairs for a gathering. You begin with the topmost chair and pile one below it until all the chairs are stacked. To tally the number of chairs in the pile, you might begin from the top and have every chair below tell you how many there are underneath it. The bottom chair tells you "1" since there isn't any beneath it. The topmost one adds itself to the next lower and calls out "2", and so on until the topmost one calls out "There are 5 in total." This "stacking and counting" idea is similar to recursion — every step of the problem depends upon the next lower one until reaching the simplest instance.

How the Recursive Code Works

In the recursive solution, the function f(n) is used to test whether n is less than 2. It returns 1 if so (because 0! and 1! are both equal to 1). Otherwise, it returns n * f(n - 1), which causes the function to call itself with a smaller argument every time. This goes on until the input is 1. When the base case is reached, the values begin to return and multiply in the positive direction, constructing the final value. The calls to the function construct a type of chain that only terminates when the smallest possible valid input is attained. This is the type of reasoning that makes recursion so strong but must be managed carefully to prevent infinite loops or stack overflows with large inputs.

Why Factorial Is a Basic Concept

Factorials run deep in mathematical computations that have to do with permutations, combinations, probability, and algorithm development. From determining the number of ways you can organize a collection of objects to optimizing problems in AI, the principle is omnipresent. In coding interviews, factorial questions are employed to measure a student's understanding of recursion, base cases, and mathematical modeling. Learning factorials through recursion also introduces students to the idea of "divide and solve", which is foundational to more advanced topics like divide and conquer algorithms, tree traversals, and dynamic programming.

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If you're searching for the easiest and most efficient way to write a recursive factorial program, this guide provides everything you need. With concise, simple code in C, C++, Java, and Python, and a well-explained explanation of the recursion logic, this solution is ideal for learners, exam preparers, or interview aspirants solving coding interviews. Learning recursion through a problem such as factorial makes you confident in problem-solving and gives you a foundation for learning more complicated recursive problems afterwards. Whether you are asked a question in a tech interview or are learning computer science from the beginning, this factorial solution is a must-have tool in your programming arsenal.