Understanding Factorial in Mathematics

The factorial of a non-negative integer n, denoted as $n!$, is the product of all positive integers less than or equal to n:

text (ISO Standard)
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n! = n × (n - 1) × (n - 2) × ... × 1

Special base case: $0! = 1$. Note that factorials grow extremely fast, so in C programming we typically use unsigned long long to prevent integer overflow for values up to $n = 20$.

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Method 1: Iterative Approach (Loop)

The iterative approach uses a standard for loop, multiplying an accumulator variable from $1$ up to n.

c (ISO Standard)
Run in Compiler.cCopy
#include <stdio.h>

unsigned long long factorialIterative(int n) {
    if (n < 0) {
        return 0; /* Factorial is undefined for negative integers */
    }
    
    unsigned long long fact = 1;
    for (int i = 1; i <= n; i++) {
        fact *= (unsigned long long)i;
    }
    return fact;
}

int main() {
    int number = 10;
    
    printf("Calculating factorial of %d (Iterative):\n", number);
    unsigned long long result = factorialIterative(number);
    
    printf("%d! = %llu\n", number, result);
    return 0;
}

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Method 2: Recursive Approach

Recursion breaks the problem into subproblems: $n! = n × (n-1)!$ with the terminating base case $0! = 1$.

c (ISO Standard)
Run in Compiler.cCopy
#include <stdio.h>

unsigned long long factorialRecursive(int n) {
    /* Base cases */
    if (n < 0) {
        return 0;
    }
    if (n == 0 || n == 1) {
        return 1;
    }
    
    /* Recursive step */
    return (unsigned long long)n * factorialRecursive(n - 1);
}

int main() {
    int number = 7;
    
    printf("Calculating factorial of %d (Recursive):\n", number);
    unsigned long long result = factorialRecursive(number);
    
    printf("%d! = %llu\n", number, result);
    return 0;
}

Sample Output

text (ISO Standard)
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Calculating factorial of 10 (Iterative):
10! = 3628800

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Complexity Analysis

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Related Guides & Algorithms

• Practice recursion with our Fibonacci Series in C program.
• Master functions and recursion stacks in Functions in C Programming.
• Test edge cases interactively in the Online C Compiler.