The factorials for real negative numbers may be defined by the integral equation, MathML. The factorials of negative real numbers are complex numbers. At negative integers the imaginary part of complex factorials is zero, and the factorials for -1, -2, -3, -4 are -1, 2, -6, 24 respectively.

Why is there no negative factorial?

Explanation: One of the main practical uses of the factorial is to give you the number of ways to permute objects. You can't permute −2 objects because you can't have less than 0 objects!

Are all factorials positive?

factorial, in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. ... Factorials have been generalized to include nonintegral values (see gamma function).