Legends say they were three:
Dead Orbit, for the most emos of us looking for a worthy substituite of the Superblack Shader.
Future War Cult, for the most conspiracy theorists not ashamed to jump around the Tower wearing a ridicolous purple.
And New Monarchy, which sucked, but had very cool Armors indeed.
But then there was Forsaken. And with it, those Factions endend into the oblivion. Rumors say that you can still see the ghosts of their Vendors around the Tower, but if you try to talk with them... they'll remain silent like only the Guardian can do...
It is said that one day content will be easy to make, and then the Factions may return... until then, waiting, you can still buy a Green Sparrow from Hamanda, if you want...
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Once upon a time there were factions. Players aligned with one of them and ranked them up through gaining XP by playing Destiny. At rank 25 a quest dropped for an exotic class item. Then we got Destiny 2 and all of that went away.