let C be the choose function, defined as:
Why can't C(n,k) have a prime factor larger than n?
I don't know much about the relationship between the binomial coefficient and prime factors and was wondering if I could just be pointed in the right direction.
Take C(47,11) for example. It is equal to 17417133617. To me this seems to be an arbitrary large number. How can I tell that this number, from the information that it is C(47,11), has no prime factor larger than 47?
The reason I have this question is that I observed this trait after solving a problem (I verified it with several testcases by writing a short Python program that finds all the prime factors of a number), but have been unable to prove it or explain why.