As with the overwhelming majority of technical terms in mathematics and the sciences, the Chinese word corresponding to English factorial is compositionally transparent — you can tell much more easily what it means by analyzing it than you can its English counterpart. (At least, by analyzing it in writing.)
Factorial is jiēchéng 階乘/阶乘, meaning "stepped multiplication". Chinese mathematics in symbols usually uses the form n! just as other languages do, but the word is sometimes written out in full, and at those time it becomes clear that it is being treated a noun. For instance: ēnde jiēchéng, written n 的階乘, and meaning 'the factorial of n'. In English, factorial can certainly function as a noun, but in the form n factorial (corresponding to n!) I think it is more natural to think of it as a suffixed function-modifier, like "five squared", "the quotient doubled", and so on. The current version of the Oxford English Dictionary (accessed on-line, 20111215) does not list this particular usage, but identifies factorial first of all as an adjective, in usage such as factorial expression, factorial function, and so on.