What does "factorial" mean?
The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.
Factorial
/fækˈtɔːɹi.əl/ adj, noun
adj, noun ·Uncommon ·Advanced level
Meaning at a glance
- Primary sense: The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.
- Grammar: factorial is listed as adj, noun.
- Nearest alternatives: combinatorial, factorial function, factorial operator, factorial product.
- Useful contrasts: gamma, nonfactorial, single-factor.
- Usage evidence: In reply, Lisa asked me to calculate 100 factorial in my head.
How to use "factorial"
- Start with the primary definition, then check the part of speech before placing the word in a sentence.
- Compare nearby synonyms to make sure "factorial" carries the exact meaning, tone, and strength you need.
- Use the example sentence as a context check. If your sentence uses the word differently, confirm that the grammar still fits.
Meaning check
- Does the word fit the sentence's grammar?
- Does it match the intended tone rather than only the dictionary definition?
- Would a simpler synonym be clearer for the reader?
- Is there enough surrounding context to prevent ambiguity?
Source and review context
This entry combines structured lexical data with WordToolSet review checks. Definitions, examples, synonyms, and usage notes may come from different source tables, so the page is designed to show evidence from more than one angle before you rely on "factorial" in a final draft.
If a word has several senses, prefer the sense that matches your sentence's grammar and surrounding context. A correct definition can still be the wrong choice when the sentence needs a different register, emphasis, or level of specificity.
Before you rely on this definition
Read the first definition as a starting point, then check the example, synonyms, and part of speech before treating "factorial" as the right word for your sentence.
If your draft is formal, technical, persuasive, or sensitive, compare "factorial" with a nearby alternative so the final choice matches both meaning and reader expectation.
Compare nearby meanings
- Use synonyms when you need a softer, stronger, simpler, or more specific word.
- Use antonyms to check the boundary of the meaning and avoid accidental contrast.
- Use the example sentence to confirm the word behaves naturally in context.
- Keep the original wording when a replacement adds complexity without improving precision.
Definition decision workflow
1. Identify the role
Check whether "factorial" is acting as adj, noun in your sentence. A definition is only useful when the grammar matches the way the word is being used.
2. Test the nearest option
Compare it with "combinatorial" and other nearby choices to see whether the sentence needs a softer, stronger, or more familiar word.
3. Confirm with context
Use the example sentence below as an evidence check, then read your own sentence out loud to catch tone or rhythm problems.
Review note: Definition pages are checked for source coverage, sentence evidence, synonym support, and editorial insight before they are treated as approval-ready pages. If the evidence is too thin, the page remains available to users but is kept out of the approval-facing indexed inventory.
Final meaning check
Before publishing a sentence with "factorial", ask whether the word helps the reader understand the idea faster. A precise word should reduce confusion, not simply make the sentence look more polished.
When the definition, synonym evidence, and example context point in the same direction, the word is usually a safer choice. When they conflict, revise the sentence or choose a clearer alternative.
Definitions
Noun
- 1 The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.
"The expression #123;#125;#95;nC#95;r means the number of combinations of n things taken r at a time. It is also written #92;binomnr, and is equal to#92;frac#123;n(n-1)(n-2)(n-3)#92;cdots#92;cdots(n-r#43;1)#125;#123;r#33;#125;or n#33;#47;r#33;(n-r)#33;, in which r#33; is read "factorial r" and denotes the product of all the integral numbers from 1 to r inclusive."
- 2 the product of all the integers up to and including a given integer wordnet
Adjective
- 1 Of or pertaining to a factor or factorial.
"I shall denote, as usual, the factorial product of the numbers up to n by n#33;, but I have found it necessary to introduce a separate notation for the products of successive even or odd numbers. I consequently definen#33;#33;#61;n#92;cdot(n-2)#33;#33;.Starting with1#33;#33;#61;1,#92;quad 2#33;#33;#61;2,it follows that, for positive values of n,n#33;#33;#61;n#92;cdotn-2#92;cdotn-4#92;cdots,where the last factor is either 1 or 2, according as n is odd or even."
- 2 Of or pertaining to a factor, a kind of business agent.
"The latter sold the goods to a customer who was cashier to certain creditors of the agents without disclosing the factorial capacity in which they acted."
- 3 Of or pertaining to a factory. dated
Adjective
- 1 of or relating to factorials wordnet
Synonyms
All synonymsAntonyms
Example
"In reply, Lisa asked me to calculate 100 factorial in my head."
Common questions
What is a synonym for "factorial"?
Common synonyms include: combinatorial, factorial function, factorial operator, factorial product, multifactorial, n factorial.
How do you use "factorial" in a sentence?
In reply, Lisa asked me to calculate 100 factorial in my head.
How do you pronounce "factorial"?
Pronounced /fækˈtɔːɹi.əl/.
Etymology
From factor + -ial.