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170 is the largest integer for which its factorial can be stored in IEEE 754 double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10 306. [citation needed]
A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k).
The factorial function of a positive integer is defined by the product of all positive integers not greater than [1] ! = (). This may be written more ...
However, the gamma function, unlike the factorial, is more broadly defined for all complex numbers other than non-positive integers; nevertheless, Stirling's formula may still be applied.
By analogy with the factorial function, a product whose factors are the integers from 1 to n, Donald Knuth proposed the name Termial function, [18] with the notation n? for the sum whose terms are the integers from 1 to n (the n th triangular number).
In mathematics, a primorial prime is a prime number of the form p n # ± 1, where p n # is the primorial of p n (i.e. the product of the first n primes). [1]Primality tests show that:
The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS). In this article, a factorial number representation will be flagged by a subscript "!". In addition, some examples will have digits delimited by a colon. For example, 3:4:1:0:1:0! stands for
In mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a composite number, or it is not, in which case it is a prime number.