Lets write a C program to find Factorial of a user input number using Recursion.
Factorial Definition: Factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n.
Important Note: By convention, Factorial of 0 is 1. i.e., 0! = 1.
Example: 5! = 5 x 4 x 3 x 2 x 1 which is equal to 120. i.e., 5! = 120.
Formula To Calculate Factorial of any positive integer number
We can calculate factorial of any number using this relationship:
num! = num * (num – 1)!
where num is a positive integer number.
Related Read:
C Program To Find Factorial of a Number
Recursive Functions In C Programming Language
Video Tutorial: C Program To Find Factorial of a Number using Recursion
[youtube https://www.youtube.com/watch?v=efcK6uNZzKw]
Source Code: C Program To Find Factorial of a Number using Recursion
#include<stdio.h> int fact(int); int main() { int num; printf("Enter a positive number to find its Factorial\n"); scanf("%d", &num); printf("\nFactorial of %d is %d.\n", num, fact(num)); return 0; } int fact(int num) { if(num) return(num * fact(num - 1)); else return 1; }
Output 1:
Enter a positive number to find its Factorial
7
Factorial of 7 is 5040.
Output 2:
Enter a positive number to find its Factorial
8
Factorial of 8 is 40320.
Logic To Find Factorial of a Number using Recursion
We ask the user to enter a positive integer number and we pass this number to a function called fact().
Inside fact() function
Inside fact() function, we check if the number is non-zero, if true, we execute the code inside if block orelse(if num is zero), then the code inside else block gets executed.
Inside if block, we add the factorial of (num-1) to the value of num.
num * fact(num – 1)
and return the result to the calling function.
Inside else block, we simply return 1. Because factorial of 0 is 1. So when num is 0, we return 1.
Example:
num | num * fact(num-1) |
---|---|
5 | 5 * fact(4) |
4 | 4 * fact(3) |
3 | 3 * fact(2) |
2 | 2 * fact(1) |
1 | 1 * fact(0) |
Value Returning – Control Shifting back.
Function | Return Value | Result |
---|---|---|
1 * fact(0) | return 1; | 1 * 1 = 1 |
2 * fact(1) | 1 | 2 * 1 = 2 |
3 * fact(2) | 2 | 3 * 2 = 6 |
4 * fact(3) | 6 | 4 * 6 = 24 |
5 * fact(4) | 24 | 5 * 24 = 120 |
Finally 120 will be returned to main() method where we call the fact() method.
Source Code: C Program To Find Factorial of a Number using Recursion and Ternary or Conditional Operator
#include<stdio.h> int fact(int); int main() { int num; printf("Enter a positive number to find its Factorial\n"); scanf("%d", &num); printf("\nFactorial of %d is %d.\n", num, fact(num)); return 0; } int fact(int num) { return( (num > 0) ? (num * fact(num - 1)) : 1 ); }
Output 1:
Enter a positive number to find its Factorial
5
Factorial of 5 is 120.
Output 2:
Enter a positive number to find its Factorial
6
Factorial of 6 is 720.
Know more about ternary operator or conditional operator, watch a separate video tutorial: Ternary Operator / Conditional Operator In C.
Memory Stack
Whenever there is a recursive function call, function instance and the memory associated with that function instance gets pushed into the stack. When any function instance returns a value, that function instance and memory associated with that function instance gets popped out or removed or gets deleted from the memory stack.
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