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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 ?
Hence, the factoral approach regards the abundance or scarcity of factors of production as the key to political action.
436) argues, "evidence suggests that political behavior, especially with regard to economic policy, is less commonly factoral (laborers as a class, capitalists as a class) than sectoral (the steel industry, the dairy farming industry).
Sectoral theorists maintain that actors resist the redeployment required for factoral mobility because changing jobs or shifting investments is unsettling.
To summarize, sectoral theory sees interdependence as producing conflict on an industry-wide basis, instead of the factoral lines envisioned by Stolper-Samuelson.
If these views are correct, then one must question mobilization arguments about the reactions, either factoral or sectoral, of local capital to foreign investments.
Factoral theory maintains that the abundance (or scarcity) of labor and capital are the key elements, while sectoral theory points to export performance and efficiency or competitiveness.
The factoral variables investigated were labor and capital.
The trends in single factoral terms of trade are more or less parallel to the trends noted for the net barter terms of trade.
Using 3-year moving averages, the author has worked out (a) net barter terms of trade (b) income terms of trade and (c) single factoral terms of trade, for the period from 1951 to 1984.
59 Single Income Factoral Terms Terms of Years of Trade Trade 1 4 5 1951-54 83.