Factorials

As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed. Feb 19, 2018 This precalculus video tutorial provides a basic introduction into factorials. It explains how to simplify factorial expressions as well as how to evaluate factorial expressions. It discusses how.

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Related to Factorials: Permutations

fac·to·ri·al

(făk-tôr′ē-əl)n.

The product of all the positive integers from 1 to a given number: 4 factorial, usually written 4!, is equal to 24 (1 × 2 × 3 × 4 = 24).

adj.

factorial

(fækˈtɔːrɪəl) mathsn

(Mathematics) the product of all the positive integers from one up to and including a given integer. Factorial zero is assigned the value of one: factorial four is 1 × 2 × 3 × 4. Symbol: n!, where n is the given integer

adj

(Mathematics) of or involving factorials or factors

fac•to•ri•al

(fækˈtɔr i əl, -ˈtoʊr-)
n.

1. the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 ∙ 3 ∙ 2 ∙ 1 = 24.Symbol: n!, where n is the given integer.

adj.

3. of or pertaining to a factor or a factory.

fac•to′ri•al•ly,adv.

fac·to·ri·al

(făk-tôr′ē-əl)

The product of all of the positive integers from 1 to a given positive integer. It is written as the given integer followed by an exclamation point. For example, the factorial of 4 (written 4!) is 1 × 2 × 3 × 4, or 24.

Noun	1.	factorial - the product of all the integers up to and including a given integer; '1, 2, 6, 24, and 120 are factorials' mathematical product, product - a quantity obtained by multiplication; 'the product of 2 and 3 is 6'
Adj.	1.	factorial - of or relating to factorials

fakultet

階乗

fatorial

fakultet

factorial

[fækˈtɔːrɪəl]

B.N → factorialm or f

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Updated February 11, 2017 Infoplease Staff

The factorial of a number is the product of all the whole numbers, except zero, that are less than or equal to that number. For example, to find the factorial of 7 you would multiply together all the whole numbers, except zero, that are less than or equal to 7. Like this:

7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

The factorial of a number is shown by putting an exclamation point after that number. So, 7! is a way of writing “the factorial of 7” (or “7 factorial”).

Here are some factorials:

1! = 1 = 1

2! = 2 x 1 = 2

3! = 3 x 2 x 1 = 6

4! = 4 x 3 x 2 x 1 = 24

5! = 5 x 4 x 3 x 2 x 1 = 120

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

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

decreasing.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 39,916,800

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600

Factorials are useful. They can show how many different ways there are to order or arrange a set of things. For example, if you have 5 books on a shelf, and want to know how many different ways there are to order or arrange them, simply find the factorial of 5:

5! = 5 x 4 x 3 x 2 x 1 = 120

This shows that you can arrange 5 books 120 different ways.

Here's a bit of trivia: mathematicians have decided that the factorial of zero, or 0!, is 1. Why? Because you can arrange a set of nothing, an empty set, in just one way—as nothing, an empty set.

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