Trials are run at all possible combinations of factor settings. The sample size is the product of the numbers of levels of the factors. For example, a factorial experiment with a two-level factor, a three-level factor and a four-level factor has 2 x 3 x 4 = 24 runs.
Full factorial designs are often too expensive to run, since the sample size grows exponentially with the number of factors.
They are typically used when the number of factors and levels are small, and when we want all possible interaction information. Hence the most commonly used factorial designs are 2k full factorials.