There are a lot of theories about where the '7' comes from for the Boeing airliners, and I am sure this has been discussed before here.
As for the '3' in the Airbus series, this is easier. The original A300 was conceived as a 300-seater, though most versions flew fewer than 300.
The A300B10 shorter version of the A300 was later designated the A310. Then a series was born !