I spent the day replacing door knobs. Odd, but the holes for the door knobs in this particular house were all a bit smaller than industry standard. Some of the old door knobs were hammered or otherwise jammed into their holes...which is probably why they broke after just a few short decades..instead of lasting forever like good door knobs should.
Most of the time was spent figuring out how to expand the size of the holes.
Anyway, the secret to replacing doorknobs is to take your key down and ask the hardware store to give you knobs that fit your key. Generally you can match keys if the knobs are made by the same manufacturer. This house in question had knobs from a variety of makers. The owner had bought two new Kwik Set knobs. The old knobs were Schlage and various nameless brands. Being kind, I ran out and bought more Kwik Set knobs so they match.