In mathematics, a factorial is what you get when you multiply a whole number by every positive whole number smaller than it. We write it with an exclamation point after the number: 5! means 5 × 4 × 3 × 2 × 1, which equals 120.

Factorials grow incredibly fast. While 3! equals just 6, and 5! equals 120, by the time you reach 10! you're already at 3,628,800. This explosive growth makes factorials useful for calculating how many different ways you can arrange things. If you have 5 books on a shelf, there are 5! (120) different orders you could put them in. With 10 books? Over 3 million arrangements.

Factorials appear in probability, statistics, and combinatorics (the mathematics of counting and arranging). They help answer questions like “How many different teams can we make?” or “In how many ways can we arrange a deck of cards?” Mathematicians define 0! as 1, which seems strange but makes mathematical formulas work correctly.

When you see that exclamation point in math, remember: it's not showing excitement (though the numbers themselves are pretty exciting). It's telling you to multiply your way down to 1.