vapilot2004 was correct in stating that the B707 was Boeing model No. 707. It went on to become an extremely successful and popular aircraft, and the 7x7 designation continued for the 727, 737, 747 etc. It was 'catchy'. The B717 designation was originally intended bor the 'lightweight' B707, the Boeing 720, but not used (I cannot remember the COMMERCIAL reason why), until Boeing's acquisition of Douglas many decades later, when B717 was used for the latest member of the DC9 dynasty.
The Airbus '300 series' designations originated with the original Airbus, the A300. The reason was no more complex than that the aircraft carried 300 passengers! Again, there was 'product identification', and all subsequent Airbus aircraft have been A3xx.
I have zero superstititions, but I'm told that the number 7 is aviation's lucky number. Maybe that's a contributory factor to Boeing's preference for the number 7. Somehow I doubt it, but feel happy flying the luckiest Boeing of all, the B777
Regards,
Old Smokey