How to Calculate a Factorial

🔢 Ever seen a number with an exclamation mark like “5!” and wondered what it means? That’s a factorial!

Factorials are super useful in math, especially in topics like probability, combinatorics, and algebra. They might look tricky, but calculating them is actually very simple.

Let’s walk through what a factorial is, how to calculate one, and where you’ll use it.

🙋 What Is a Factorial?

A factorial, written with an exclamation mark (!), means multiplying a number by every whole number less than it down to 1.

So:

5! = 5 × 4 × 3 × 2 × 1 = 120

In plain English:
Take the number, multiply it by the one just below it, and keep going until you hit 1.

🧮 Factorial Formula

Here’s the formula:

n! = n × (n - 1) × (n - 2) × ... × 1

Where n is any whole number greater than or equal to 0.

Bonus:

0! = 1 (by definition)

It might seem strange, but it makes everything in math work out nicely — especially in probability formulas.

📋 Examples

3! = 3 × 2 × 1 = 6
4! = 4 × 3 × 2 × 1 = 24
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

As the numbers get bigger, factorials grow really fast!

🎯 Where Are Factorials Used?

• Probability and statistics: like calculating permutations and combinations
• Algebra and calculus: in binomial expansions or Taylor series
• Computer science: recursion and algorithm complexity
• Math puzzles and logic problems

For example:

How many ways can you arrange 4 books on a shelf?
Answer: 4! = 24 ways

✅ Quick Tips

• Factorials only work for non-negative whole numbers
• 0! is always 1, not 0
• They get large very quickly — use a calculator for anything above 10!