What does factorially mean?
"Factorially" is an adverb used chiefly in mathematics and computer science to describe something calculated in terms of factorials — the products obtained by multiplying all whole numbers from 1 up to a given number. It most often appears when discussing how quantities grow: because multiplying each new integer produces increasingly enormous results, saying that something "grows factorially" conveys explosive expansion far faster than ordinary exponential growth. For instance, the number of ways to arrange n items increases factorially with n, which is why problems involving permutations become computationally overwhelming very quickly. The word carries a precise, technical tone and is rarely heard outside academic or computational contexts, though it occasionally serves figuratively to emphasise staggering speed of increase. Its root is the Latin "factor", meaning a maker or doer, which entered English through mathematics to denote a quantity multiplied into another.
adverbIn a manner relating to or involving factorials, the products of all positive integers up to a given number. By extension, it can describe growth or increase at an extremely rapid rate comparable to factorial expansion.
- (Mathematics) In terms of factorials; by multiplication of all positive integers up to a given number.
- At a rate of increase comparable to factorial growth; extremely rapidly.
"The number of possible orderings grows factorially as more items are added to the list."
"A deck of cards can be arranged 52! ways, a figure computed factorially."
"The search space expands factorially with each additional task, quickly rendering brute-force solutions impractical."
Factorial growth outpaces exponential growth so quickly that by just 20 items, the number of possible arrangements exceeds the number of seconds in two billion years.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of factorially
"Factorially" derives from "factorial", a term coined in mathematics in the early 19th century from Latin "factor", meaning 'one who makes or does', from the verb "facere" ('to make'). In arithmetic, a factor is a number multiplied by another, and the adjective "factorial" came to denote the product of a series of such factors. The adverb formed with the standard suffix "-ly" and remains closely tied to its mathematical sense, sharing its origin with related words such as "factor", "factory" and "manufacture".
How factorially is actually used
Primarily a technical term used in mathematics, computer science, and combinatorics; outside these fields it is rare and may be replaced informally by 'exponentially', though the two describe different growth rates.
Easily confused with factorially
'Exponentially' describes growth by repeated multiplication by a constant base (2, 4, 8, 16…), while 'factorially' describes the faster growth produced by multiplying successively larger integers (1 × 2 × 3 × 4…).