⟩ Why does not Fortran have intrinsic functions for something as simple as factorial?
Two reasons. Factorial isn't all that common in heavy duty scientific and engineering applications. When it does occur, it almost always in a context where it is more computationally efficient to generate it as you go. You need 2! first then 3!, then 4!, etc. You are basically stuck doing a factorial within the context of a do loop unless you get really good and learn to write "recursive functions", but then you are just fooling yourself and writing another form of do loop. When you are taking the factorial of a large number and don't need an exact answer you can resort to Stirling's Approximation. A Fortran statement that will load the value of this approximation into the variable nfact is.