**A variable is a symbol, often written as a letter of the alphabet that stands for a number that can vary in value. For example, take your age. That varies every year, doesn’t it? This year your age may be, say 21. If so, in 365 days your age will be 22. Another 365 days after that and your age will be 23.**

*What are factorials?*Thus age is a function of time. For you, we can write right now:

A = 21

If the number of years that pass equals n, then for next year, n = 1 andA_{n} = 21 + n

A₀ = 21 + 0 = 21

A₁ = 21 + 1 = 22

A₂ = 21 + 2 = 23

A₃ = 21 + 3 = 24

## What Are Factorials?

Now there is nothing special about the letter A. It can be replaced by any other symbol the reader may choose. So let’s choose a new variable symbol, F. We choose to follow this symbol with, of all things, an exclamation point (!). We define this symbol to mean the mathematics operation factorial. What is a factorial?Written F! it means a product of the form

F(F‒1)(F‒2)(F‒3)… until we reach the value 1.Thus, if F = 7,

F! = 7(7‒1)(7‒2)(7‒3)(7‒4)(7‒5)(7‒6) = 7(6)(5)(4)(3)(2)(1) = 5040

## It’s Your Turn!

Problem: Solve these factorials: F = 3, F = 5, F = 11. Write out the steps.**[Answers]** 6; 120; 39,916,800

**Note:**You might also enjoy Mathematical Powers – A Simple Insight**References:**

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I don’t actually recall being taught factorials in school, I only learned about them from another student when at university, yet once you know about them, they seem like a useful everyday piece of maths.