You claim that factorial experiments make highly economical use of experimental participants, but I was taught factorial experiments require massive sample sizes to power. Can you explain this discrepancy?

This is explained on our Informal Introduction to Factorial Experiments web page and in Chapter 3 of Collins (2018). Very briefly, you may be thinking of a factorial experiment as a many-armed RCT. It isn’t. The logical underpinnings of the factorial experiment are different from those of the RCT, and therefore the approach to powering the two designs is different. In an RCT, all else being equal, power is driven by the per-arm sample size. By contrast, a factorial experiment can have very small per-condition sample sizes as long as the overall sample size per level of each factor is sufficiently large.

Reference

Collins, L.M. (2018). Optimization of behavioral, biobehavioral, and biomedical interventions: The multiphase optimization strategy (MOST). New York: Springer.