In data analysis and manipulation, a factorial is essentially a permutation where a factor B is multiplied by every other number below it down to 1. The interaction effect between each variable of a factorial permutation is that as the number you choose as factor B gets larger, the effect size increases. One of the most complex yet simple effects in algebra, a factorial can be very useful for data analysis, conducting a factorial experiment, or testing probability theory in your R code.
The main effect of including a factor variable in your R code is to create a non linear model, as once again the effect size increases with a larger number in the place of that factor variable. The factorial function itself is simple, but it is the applications to experiment design, sample size, treatment levels, error bars, and so much more that make it a great function to use in your data frame, residual plot, or interaction plot.
There are limits to the application of factorial design, as it will not work with a negative number, categorical variable, or mean calculations for example. It is mainly used to cause simple effects on a dependent variable in a data frame or algorithm, in contrast to many other data manipulation functions.
There is a simple function available for calculating a factorial in R.
The function can accept a numeric value or a vector of numeric values. here is a simple example.
# factorial in R > factorial(3)  6 > factorial(5)  120 > factorial(8)  40320 > factorial (c(3,4,5))  6 24 120