Factor analysis only applies to tests one puts into a group of tests. You get out only what you put in. Between any two tests you could put in another. So recent reactions to intelligence tests have included attempts to relate intelligence to matters outside a group of tests, for example the everyday environment or the results of brain damage. The three parts are components of intelligence, experience and the use of context.
Every horse has one more tail than no horse.
Further, we need skills useful in acquiring new knowledge. Sternberg expands on this aspect of intelligence, in three ways. We need at times to adapt to our environment. We need to select from the environment what will fit us. We need to be able to shape our environment to fit us.