Aren't we talking about geared turbofans, as described in the article and http://en.wikipedia.org/wiki/Geared_turbofan ? Geared turbofans, unlike the ungeared GEnx, presumably have gears in gearboxes.
The person I replied to implied that all turbofan engines have gearboxes, that gearing was necessary to have the fan rotate at a slower speed than the "main engine". In reality, the vast majority of the turbofan engines currently used in commercial aviation do not have gearboxes. The engines referred to in the wikipedia article you cite are still in development or just entering production.
What the current generation of engines have is two or three co-axial shafts rotating at different speeds.
The difference in shaft speeds is achieved by varying the size, shape and placement of the turbine blades connected to the shaft, not with a gearbox.
(And a single gear in isolation would be pointless. By definition, the purpose of a gear is to mesh with another gear.)
Here's an informative video: http://www.youtube.com/watch?v=zy4A-z2WKhw