🔢 Factorial Calculator
Factorial result will appear here…
📌 Understanding Factorials
The factorial of a non-negative integer n (denoted by n!) is the product of all positive integers less than or equal to n. By definition, 0! = 1.
📌 Examples of Factorial Calculation
| Number (n) | Factorial (n!) |
|---|---|
| 0 | 1 |
| 1 | 1 |
| 5 | 120 |
| 7 | 5040 |
🔧 Practical Applications of Factorials
1. Combinatorics: Factorials are used to calculate permutations and combinations.
2. Probability: They help in determining probabilities in various scenarios.
3. Mathematical Analysis: Factorials appear in series expansions and other mathematical formulas.
❓ FAQs
Q1: What is a factorial?
✅ The factorial of a non-negative integer n (denoted by n!) is the product of all positive integers up to n, with 0! defined as 1.
Q2: Can I calculate the factorial of a negative number?
✅ No, factorials are only defined for non-negative integers.
Q3: Which method should I choose?
✅ The iterative method is straightforward and shows each multiplication step, while the recursive method uses a function that calls itself. Both yield the same result.
Q4: How fast does a factorial grow?
✅ Factorials grow very rapidly, much faster than exponential functions.
Q5: Is there a limit to how large a factorial can be calculated?
✅ In JavaScript, very large factorials may exceed the maximum safe integer value. For huge numbers, specialized libraries or approximations (like Stirling’s formula) are needed.