Determine the largest 3 - digit prime factor of 2000 C 1000.

n C r denotes the number of combinations of n things taking r at a time.

Isn't 2000 C 1000 just equal to:

2000 * 1999 * 1998 * ... 1002 * 1001?

It seems to me that this is divisible by every prime less than 2000.

The largest 3 digit prime = 997

I must be missing something.