# Definition of factorial in English:

## factorial

### noun

Mathematics
• 1The product of an integer and all the integers below it; e.g. factorial four (4!) is equal to 24.

• ‘They learned of each other's discoveries because each of them communicated his work to James Stirling, whose approximation for the factorial is a special case of the Euler-Maclaurin summation.’
• ‘Stirling wrote to De Moivre pointing out some errors that he had made in a table of logarithms of factorials in the book.’
• ‘Now Stirling's formula is a classical approximation for the factorial function, and factorials are one way to evaluate binomial coefficients.’
• ‘The experiment was a completely randomized design, with eight treatment combinations, forming a 4 x 2 factorial (four clones and two watering regimes) with five plants in individual pots per treatment combination as replication.’
• ‘The gamma function is undefined for zero and negative integers, from which we can conclude that factorials of negative integers do not exist.’
1. 1.1 The product of a series of factors in an arithmetical progression.
• ‘‘A factorial is the product of consecutive numbers from 1 to that particular digit and is represented by placing a‘!’’
• ‘In the proof below, we use the fact that e is the sum of the series of inverted factorials.’

Mathematics
• Relating to a factor or factorial.

‘a factorial design’
• ‘Around 1926, a British statistician, Ronald Fisher, while working in the field of agriculture, developed a new form of experimentation called two-level factorial design.’
• ‘Experimental designs involving factorial combination of multiple independent variables call for some inventiveness when it comes to graphical presentation of data.’
• ‘Our trial was of factorial design in order to compare three types of treatment within a single trial, in order to derive the maximum amount of data from the minimum number of patients.’
• ‘One possible approach to make this search more systematic is the use of factorial design, which involves a set of experiments intended to identify important effects and interactions.’
• ‘A 2 x 4 x 12 factorial design was used to assess the effects of light, temperature and month, respectively, on the germination of Spergularia marina seeds.’

/fakˈtɔːrɪəl/