Factorial designs with only two-level factors have a sample size that is a power of two (specifically 2f where f is the number of factors). When there are three factors, the factorial design points are at the vertices of a cube as shown in the diagram below. For more factors, the design points are the vertices of a hypercube.
Full Factorial Design
JMP Learning Library – Designed Experiments
Watch a brief video on designing and analyzing a variety of experiment types, including full factorial, fractional factorial, screening and more.