This series of worksheets help students begin to understand the use and math behind factorial notation.

These worksheets will introduce the concept of factorial notation to students. The symbol (!) just indicates that an equation calls for multiplication. While many people see factorials and have no idea why they use an exclamation point others see them as clear and concise measures from 1 to n. Expressions that are included in sigma notation often have the inclusion of this type of notation. This set of worksheets will get you ready for this. There are two separate lessons demonstrating how to solve factorial equations. Included are two sets of lessons, quizzes, review sheets, and practice worksheets.

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Factorial Notation Lesson

Factorial Notation Lesson

Follow the steps to learn how to determine the factorial of a number. Example: Determine the value of 7.

Factorial Notation Worksheet 1

Factorial Notation Worksheet 1

Determine the values for these 10 equations. They are very basic in nature to help you learn the concepts and not let the math get in the way. Example: 2! + (8 - 3)!

Worksheet 2

Worksheet 2

Here are 10 more problems for you to work on. Example: 4! + (10 - 4)!

Review Sheet

Review Sheet

Follow the steps to review how to determine the value of a factorial. Here is an example problem: 5! - 3!



There are 10 problems. This are not basic problems and they will require you to complete the equations.

Do Now Worksheet

Do Now

You will be given 3 problems that you will complete and then go over with your teacher. If you do not get the correct answer, use the second column to document it.

Factorial Notation Lesson 2

Factorial Notation Lesson 2

This lesson will walk you through more moderately advanced steps.

Basic Operations Worksheet 1

Basic Operations Worksheet 1

You will determine the output of simple equations that include factorial aspects.

Worksheet 2

Worksheet 2

You will have more work on simple problems that gives you more experience. These example problems look like this: 10! + 4!

Homework Sheet

Homework Sheet

This will provide you with a chance to learn anything that you may have missed along the way.


Factorial Quiz

What are you missing in these types of problems? You will find out now. Be critical of yourself and see what you need more work on.

Factorial Notation Do Now Worksheet

Factorial Notation Do Now

This is another full classroom activity for you to ponder when you are working on this skill.

What is Factorial Notation?

Factorial notation is denoted by the symbol "!". We can use the letter "n" to denote any positive integer or number. When we want to talk about the factorial of that integer, we denote it with "n!".

The factorial of any integer is defined as the product of all the positive numbers that come before, or are equal to, the integer.

So, if we were to find n! we can define it in the equation:

n! = n x (n-1) x (n -2) x (n-3) …… x 3 x 2 x 1


n! = 1 x 2 x 3 x 4 x ………... x n

Example: Find the end value of 6!

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Factorial notation has many different applications:

  • They are used to count permutations: sequence of numbers.
  • They are used in formulas of combinatorics: different order of objects.
  • They are used in the binomial theorem
  • They are used in Newton's identities
  • They appear in denominators in exponential functions

The best way of perfecting this type of math is to practice different questions on them. Let's see how to apply this type of math.

Example: Find the end value of 8! .

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

And so, 8! = 40320

History of the Factorial Notation

Fabian Stedman, a British author, was the first to define factorial in 1677. He described it as comparable to change ringing. Change Ringing was a musical performance in which multiple tuned bells were rung. In 1808, Christian Kramp, a mathematician, invented the symbol for factorial "!".

Louis Arbogast first used the term "Factorial" in 1800. But this type of math had existed decades before that. Evidence of it goes far back as 300 BCE.

The Factorial Table

Once you've understood what the symbols mean, you can solve any question. But, after some time, it gets tedious. Some teachers prefer their students to memorize a fixed number of factorials of integers. For instance from 0 to 10. Like the multiplication table (times table), it makes it easier to solve questions.

Integer (n) Factorial (n!)
0 1
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3628800

The Factorial of Zero

If you look at the table above, you will see that the value of zero factorial is 1. This often confuses a lot of people. How can it be one?

Remember that factorial notations tell us the possible number of combinations with numbers equal to or less than that number. Hence, by definition, the value of 0! should be one.

Since there is no number less than zero, but zero itself is a number, there is only one possible combination on how the value can be arranged.


Factorial notations are nothing more than just the number of possibilities for several objects to be arranged. Once you've figured out how to identify and solve these types of problems, there is no question that you cannot do.

Remember to practice what you've learned. The key to perfecting any math formula is to practice.