Even though it is commonly used for examples, the factorial function isn't all that useful in practice. The numbers grow very quickly, and most problems that include the factorial function can (and should) be computed in more efficient ways.
A trivial example is computing binomial coefficients. While it is possible to define them as
choose n k = factorial n `div` (factorial k * factorial (n-k))
it is much more efficient not to use factorials:
choose n 0 = 1
choose 0 k = 0
choose n k = choose (n-1) (k-1) * n `div` k
So, no, it's not included in the standard prelude. Neither is the Fibonacci sequence, the Ackermann function, or many other functions that while theoretically interesting are not used commonly enough in practice to warrant a spot in the standard libraries.
That being said, there are many math libraries available on Hackage.