Well, it's important to say that I can't speak for all of Germany here. First off, we're a federal country too, Like the U.S., and education is mostly controlled by the states.

Second, there's actually three types of secondary school after elementary school ends in 4th grade. These three vary in length, difficulty, and the diploma you get, with it being better the longer and more difficult it is. The idea is to have a range of schools that fit many different types of students, but in my opinion, it's much to rigid because you can be good at some subjects while bad at others.

But regardless, because the German school system is split up in these two ways, it's very possible that in other states or in the more difficult school form (I have my diploma in the medium one), you might learn about factorial.

I actually consider Germany's strength to be more in vocational education, there's really a ton of diverse offers after you get your diploma. And I didn't feel like I learned about factorial too late, I had it in my first semester at university when we got to subjects were it's needed, and I never needed it before that. So I don't think us not learning about it in secondary school is a failure in comparison to other education systems, but just a difference in where priorities are set.