Find Factorial of a Number Using Recursion

#include <stdio.h> #include <conio.h> // function prototype int fact(int n); void main() // Turbo C accepts void main { int num, result; clrscr(); // optional: clears the screen printf("Enter the number: "); scanf("%d", &num); result = fact(num); printf("The factorial is %d", result); getch(); // wait for key press before exit } int fact(int n) // recursive factorial function { if (n <= 1) return 1; // base case else return n * fact(n - 1); // recursive call } Output

Calculation & Dry Run

This section explains the mathematical calculation and a step-by-step dry run (call stack) for the recursive factorial function. Example input used: 5.

Mathematical Calculation

Factorial definition:

n! = n × (n-1) × (n-2) × … × 1

So for n = 5:

5! = 5 × 4 × 3 × 2 × 1

= 120

Dry Run (Function Call Stack)

Assume the program calls fact(5). The recursion expands until the base case (n <= 1) is reached. Each step waits for the inner call to return.

Step	Function Call	Action / Return Value	Stack Status
1	fact(5)	Needs 5 × fact(4)	fact(5) waiting for fact(4)
2	fact(4)	Needs 4 × fact(3)	fact(5) → fact(4)
3	fact(3)	Needs 3 × fact(2)	fact(5) → fact(4) → fact(3)
4	fact(2)	Needs 2 × fact(1)	fact(5) → fact(4) → fact(3) → fact(2)
5	fact(1)	Base case reached, returns 1	Inner-most call returns
6	fact(2) resumes	Returns 2 × 1 = 2	fact(5) → fact(4) → fact(3)
7	fact(3) resumes	Returns 3 × 2 = 6	fact(5) → fact(4)
8	fact(4) resumes	Returns 4 × 6 = 24	fact(5)
9	fact(5) resumes	Returns 5 × 24 = 120	Stack empty

Final Output

The factorial is 120

Code (C) — For Reference

#include <stdio.h> int fact(int n) { if (n <= 1) return 1; else return n * fact(n - 1); } int main(void) { int num, result; printf("Enter a number: "); scanf("%d", &num); result = fact(num); printf("The factorial is %d\n", result); return 0; }