and the product of computers not any better than a good pocket calculator ...
The computer systems involved in the Apollo 11 mission, main guidance computer on the Command Module and the one on the LEM, combined had far less processing power than a basic modern mobile phone. They both worked well and many ways can be regarded as the predecessors of the modern fly by wire systems in use today.
From NASA history
With a lunar orbit rendezvous mission, more than one computer would be required, since both the CM and the lunar excursion module (LEM) needed on-board computers for the guidance and navigation function. The CM's computer would handle the translunar and transearth navigation and the LEM's would provide for autonomous landing, ascent, and rendezvous guidance.
Ch2-3
M.I.T. Apollo Guidance Computer