Factorial facts for kids
The factorial of a whole number n, written as n!, is found by multiplying n by all the whole numbers smaller than it, down to 1. For example, the factorial of 4 is 24, because 4 × 3 × 2 × 1 = 24. So, we can write 4! = 24. For special math reasons, 0! is equal to 1.
Contents
What is Factorial?
Factorial helps us figure out how many different ways we can arrange a certain number of items. Imagine you have a few different things, and you want to know all the possible orders you can put them in. Factorial is the tool for that!
Arranging Things with Factorial
Let's say you have three letters: A, B, and C. How many ways can you arrange them?
- ABC
- ACB
- BAC
- BCA
- CAB
- CBA
There are 6 different ways! Factorial shows us this:
- For the first spot, you have 3 choices (A, B, or C).
- For the second spot, you have 2 choices left.
- For the last spot, you have only 1 choice left.
So, you multiply the choices: 3 × 2 × 1 = 6. This is the same as 3!.
How Factorial Grows
The factorial number grows very, very quickly! Even with a small number like 10, the factorial is huge.
- 10! = 3,628,800 ways to arrange 10 items.
Imagine trying to list all those arrangements! Factorial makes it easy to find the total number.
Factorial and Recursion
Factorial is a great example of something called recursion. This is when a process repeats itself. You can write 3! as 3 × (2!). Then, 2! can be written as 2 × (1!). And 1! is 1 × (0!). Since 0! is 1, it stops there. So, n! can also be defined as n × (n-1)!, with 0! = 1. It's like a set of Russian nesting dolls, where each one helps define the next.
What Factorial is Not
The factorial function is not used for negative numbers. It only works for whole numbers that are zero or positive.
Related pages
Images for kids
-
Absolute values of the complex gamma function, showing poles at non-positive integers
-
TI SR-50A, a 1975 calculator with a factorial key (third row, center right)
.jpg)
See also
In Spanish: Factorial para niños
