Also found in: Dictionary, Thesaurus, Medical, Legal, Financial, Wikipedia.
Related to factorial: Factorial design


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



The factorial of a given natural number n is the product of all the natural numbers less than or equal to n. The factorial of n is denoted usually by n! Thus,

n! = 1 × 2 × ... × n

For large n an approximate expression for n! is given by Stirling’s formula. The number of permutations of n things taken all at a time is the factorial of n.


The product of all positive integers less than or equal to n; written n !; by convention 0! = 1.


The mathematical function that takes a natural number, N, and returns the product of N and all smaller positive integers. This is written

N! = N * (N-1) * (N-2) * ... * 1.

The factorial of zero is one because it is an empty product.

Factorial can be defined recursively as

0! = 1 N! = N * (N-1)! , N > 0

The gamma function is the equivalent for real numbers.


The number of sequences that can exist with a set of items, derived by multiplying the number of items by the next lowest number until 1 is reached. For example, three items have six sequences (3x2x1=6): 123, 132, 231, 213, 312 and 321. See factor and IFP.
References in periodicals archive ?
In this work, to obtain the available tensile strength, Optimal values of input variables were evaluated by using two level factorial experimental design and response surface.
Medidas de adecuacion muestral y analisis factorial exploratorio
For the second level confirmatory factorial analysis, the structural model is added, which relates the latent factors of the previous part to the "Job Satisfaction" factor, whose matrix structure is explained as:
The optimal conditions obtained with factorial design, 50% concentration of wastewater and a 7-day-production period, were fixed as production parameter and validated.
Fractional factorial design method is very effective tool for the parametric optimization of welding parameters.
Therefore, the factorial analysis showed that of 55 items that comprised the assessment instrument of teaching styles, 17 belonged to the dynamic teaching style, only 6 belonged to the dynamic and analytical styles, 1 belonged to the dynamic and systematic styles, and 1 belonged to the dynamic and practical styles, totaling 25 items (30% of items that composed the questionnaire).
Let a triple factorial experiment conducted in CRD with factors [alpha], [beta] and [gamma] considered in a, b and c levels, respectively, replicated J times.
El analisis factorial es una tecnica de reduccion de datos que sirve para encontrar grupos homogeneos de variables a partir de un conjunto usualmente grande de variables.
Sebi has accused Factorial of fraudulent and unfair trade practices regulations, saying it traded on the basis of its access to 'unpublished price sensitive information' (UPSI).
Furthermore, it should be noted that the identification of the factorial structure of the scales, through Exploratory Factor Analysis, is an important prerequisite for more refined analyzes, such as Confirmatory Factor Analysis (Pilati & Laros, 2007).
Admitting factorial analysis of variable of discrimination strategy: