If you want to read the NASA history of computer development for manned systems, go here. The equivalent history for umnanned systems is here.

Consider the technology of the era. RAM was made from iron cores. It was non-volitile (a good thing when you remember that Apollo 12 was struck by lightning twice during launch. Talk about your power surges! At the same time, integrated circuits were still a fairly immature technology.

Consider these excepts from the Apollo computer hardware section.

"The Apollo Guidance Computer was fairly compact for a computer of its time. The CM housed the computer in a lower equipment bay, near the navigator's station. Block II measured 24 by 12.5 by 6 inches, weighed 70.1 pounds, and required 70 watts at 28 volts DC. The machine in the lunar module was identical.

Crew members could communicate with either computer using display and keyboard units (DSKY, pronounced "disky"). Two DSKYs were in the CM, one on the main control panel and one near the optical instruments at the navigator's station. In addition, a "mark" button was at the navigator's station to signal the computer when a star fix was being taken. A single DSKY was in the lunar module. The DSKYs were 8 by 8 by 7 inches and weighed 17.5 pounds. As well as the DSKYs, the computer directly hooked to the inertial measurement unit and, in the CM, to the optical units."

...

"MIT's original design called for just 4K words of fixed memory and 256 words of erasable (at the time, two computers for redundancy were still under consideration)50. By June 1963, the figures had grown to 10K of fixed and 1K of erasable51. The next jump was to 12K of fixed, with MIT still insisting that the memory requirement for an autonomous lunar mission could be kept under 16K 52! Fixed memory leapt to 24K and then finally to 36K words, and erasable memory had a final configuration of 2K words."

...

"The actual composition of the memory was fairly standard in its erasable component but somewhat unique in its fixed component. The erasable memory consisted of coincident-current ferrite cores similar to those on the Gemini computer, and the fixed memory consisted of core rope, a high-density read-only memory using cores of similar material composition as the erasable memory but of completely different design. MIT adopted the use of core rope in the original Mars probe computer design and carried it over to the Apollo53. Chief advantage of the core rope was that it could put more information in less space, with the attendant disadvantages that it was difficult to manufacture and the data stored in it were unchangeable once it left the factory."