factorial

US /fækˈtɔriəl/ UK /fækˈtɔːriəl/ See IPA manual

Meanings

1

noun
the product of all positive integers up to a given number

The factorial of five is one hundred and twenty.

Thesaurus

Word family

Related forms factorfactorizefaction

Etymology

From factor + -ial. Factor derives from Latin factor ('doer, maker'), from facere ('to do, make'). The mathematical sense was coined in the early 19th century.

factor Latin facere Latin

View etymology graph ->

Topics

Word Formation & Derivatives General Vocabulary

External links

# factorial

**Type:** Word
**Level:** C2+
**Part of speech:** noun
**IPA (US):** /fækˈtɔriəl/
**IPA (UK):** /fækˈtɔːriəl/

## Meanings
1. the product of all positive integers up to a given number

## Examples
- The factorial of five is one hundred and twenty.

## Related Forms
- factor
- factorize
- faction

## Roots and Affixes
- Root: factor
- Root: facere

## Etymology
From factor + -ial. Factor derives from Latin factor ('doer, maker'), from facere ('to do, make'). The mathematical sense was coined in the early 19th century.

## AI Etymology
Factorial is from factor + -ial. Factor derives from Latin factor ('doer, maker'), from facere ('to do, make'). The mathematical sense was coined in the early 19th century. Important recorded forms include factor (Latin) and facere (Latin). Morphologically, the word is a built form whose named elements carry part of the historical sense. The current sense covers the product of all positive integers up to a given number. The wider family includes related words such as factor, factorize, and faction.

## Topics
- Word Formation & Derivatives
- General Vocabulary

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