The first X-Factor team was comprised of the original X-Men; Angel (aka Archangel), Beast, Cyclops, Jean Grey (Marvel Girl) and Iceman, They left Professor X's team when he placed their old nemesis, Magneto, as the team's leader. The new 'X-Factor' team set up in business as mutant-hunters-for-hire, posing as non-powered humans. This was pure pretense; the mutants that X-Factor captured were instead trained to use their powers and to blend with society.
For a time, the team would also go into action in costume, posing as mutant outlaws known as the 'X-Terminators', until this ruse was felt to cause more harm than good.
The original members of the team later rejoined the X-Men, and the US Government formed a new team under the X-Factor name. Other incarnations of the team have been formed since, bringing together various members of government teams.