factorial
noun · adjective
Simple meaning
The product of all the integers up to and including a given integer.
Pronunciation
Say it like this:
faktawreeuhlSay the bold part a little louder.
IPA pronunciation (US)
fækˈtɔɹiəl
This word is pronounced essentially the same in American and British English, so one transcription covers both.
IPA (International Phonetic Alphabet) is a standard way of writing speech sounds.
Definition
Everyday modern meanings first, grouped by part of speech.
noun
mathematicscombinatorics
The product of all the integers up to and including a given integer
“1, 2, 6, 24, and 120 are factorials.”
mathematicscombinatorics
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.
adjective
Of or pertaining to a factor, a kind of business agent.
Word at a Glance
- Difficulty
- C2 · Proficient (estimated)
- Frequency
- Rare
- Formality
- Technical
- Typical Use
- Varies by meaning
Word Aura™
How this word commonly comes across.
Aura for this meaning
This meaning: The product of all the integers up to and including a given integer
Used this way, factorial is a specialist word that usually carries little praise or criticism of its own. This is a mathematical use: it is defined precisely and belongs to working with figures and calculations rather than to ordinary conversation.
“1, 2, 6, 24, and 120 are factorials.”
- Emotional tone
- Neutral
- Formality
- Specialist/technical
- Intensity
- Not strongly marked
- How common
- Specialized
- Connotation
- Clinical and technical
- Usage feel
- Technical and specialized
Where it naturally appears
- Mathematics
- Geometry
- Academic writing
- Education/classroom
Usage note
In general conversation this sense usually needs explaining — outside its field, people reach for a plainer word.
Word Aura describes common impressions, not a measurement. Tone changes with sentence, speaker, relationship and situation.
More ways to use factorial
- “1, 2, 6, 24, and 120 are factorials.”noun
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Common Patterns and Combinations
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Word Family
Related forms, grouped by how they connect.
Word family
Words built from the same root.
A plant consisting of one or more buildings with facilities for manufacturing.
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Dictionary data from Wiktionary via the Free Dictionary API. Simple meanings, combinations and word intelligence are built from verified reference data, no AI is used to load this page.