TRIGGER WARNING: Ivy League humblebragging
Facebook Graph API Explorer gave me a little bit of insight into what their process must have been like when they were first getting big. Right now, if you make a new account your id number will be very long and not have much correlation with anything. If your friend made an account at the same time your numbers would be very different.
My id # is around 120,000. If you were at Columbia and got your Facebook account at the same time I did, your account id would be in that range. It's true for my friends. Generally, the older you are the lower you are in this range, the younger the higher.
I worked with someone who went to Cornell, his id number was around 450,000. He had his account for a year longer than I did. His friends had the same cluster, just around that number.
Clearly, at some point Facebook tried to carve up the id space and shard based on that -- surely, no one would have friends from other schools! (It is worth remembering you originally needed a college email, and that the school networks use to be a lot tighter than they are now.)