Factor Three was a subversive organization of superhuman mutants that sought to conquer Earth. Its founder and leader, the Mutant Master, unbeknownst to his followers, was actually a member of the alien Sidri race, who bear a resemblance to Earth's octopus. By disguising himself in human form and posing as a mutant human being, the Mutant Master was able to assemble an organization of mutants to aid him in his plans for world conquest.
The Mutant Master believed that there were two nuclear "super-power" nations on Earth: the United States and Russia. He intended his organization to become Earth's third "super-power," hence its name, "Factor Three."
Factor Three abducted the mutant Banshee and strapped an apparatus to his forehead which would explode should he try to remove it or disobey orders. Factor Three later sent the Banshee and a non-mutant agent of Factor Three known as the Ogre to New York to attempt to abduct Professor Charles Xavier, the mentor of the X-Men. The X-Men thwarted the scheme and captured the Ogre, and Xavier freed the Banshee from his servitude. In gratitude the Banshee told them what little he knew about Factor Three.
Presumably, the Ogre escaped, whereupon he was instructed by Factor Three to return to one of their hideaway in Burton Canyon, Colorado. There, he was instructed to monitor the phenomenally powerful mutant, Humus Sapien, to ensure that he would remain dormant.
Much later, Factor Three returned to find the Ogre still waiting for them. Ogre helped them with the details of daily life, while the other members formed their latest plan. The Ogre was instructed to stay behind, to watch over Humus Sapien and wait for their return. (As Factor Three ultimately disbanded after their final defeat, Ogre remained hidden in Burton Canyon for many years until being discovered by the Thunderbolts, who hoped to appropriate the abandoned base for their own.)
In the meantime, Factor Three freed the X-Men's enemy, the Juggernaut, from captivity to distract the X-Men while they succeeded in abducting Xavier.
Then, the Banshee located the European headquarters of Factor Three just before he was captured himself. The X-Men went to Europe to invade the base only to be captured by Factor Three and taken inside. There they first encountered the Mutant Master, in his human disguise, and his second-in-command, the Changeling. The X-Men also learned that their old adversaries, the Blob, the original Mastermind, Unus the Untouchable, and the Vanisher, were all agents of Factor Three. The Mutant Master revealed his plan to trigger a nuclear war between the United States and Russia that would wipe out the human race.
The X-Men escaped Factor Three's mountain lair just before the Mutant Master blew it up, and they succeeded in thwarting his scheme to start World War III. Meanwhile, at Factor Three's alternate base, the Changeling discovered that the Mutant Master's real purpose was to wipe out both humanity and mutantkind. The Changeling freed Professor X and the Banshee, whose sonic scream shattered the Mutant Master's disguise, revealing him to be a green, many-tentacled alien. The X-Men and Factor Three's mutant agents joined forces to fight the Mutant Master, who committed suicide to avoid capture. With his demise, Factor Three came to an end.