the crop factor and aperture are 2 different things, although both are related to the focal length of a lens.
When cropped body DSLRs were first developed, most available lenses were for full frame 35mm film SLRs. The concept of crop factor or focal length multipliers was used so photographers could understand what they would get using a full frame lens on a cropped sensor body. Even now, for lenses that can be used on a full frame or cropped body DSLR the focal length is always quoted for full frame.
There are many detailed explanation all over the web on crop factor, and one of the best I've seen is at
in my simplistic explanation: if you put a 100mm lens on a cropped body it is still a 100mm lens and the focusing distance to the sensor is identical to a full frame body - we just capture the centre part of the image area of the lens instead of it all. We effectively reduce the angle of the field of view which has an identical effect to zooming.
The aperture value of a lens is directly related to the diameter of the 'hole' that lets the light through. The diameters are set to either 1/2 or double the area of the hole, letting in 1/2 of twice as much light. To get consistency between lenses the aperture (hole size) is calculated using the focal length. This way a lens at f/2 lens will let the same proportion of light whether its a 100mm of 25mm lens
Note I used f/2 not f2. Over the years for convenience the / has been left out, but it means exactly that: f/2 so for a 100mm lens means diameter of the aperture is 50mm, at f/4 aperture will be 25mm etc (ignoring the high skill of lens and glass designers.) This also explains why f/2 lets in more light than f/8 - for a 100mm lens the aperture is 50mm and 12.5mm diameter respectively)
So say we start with a 100mm lens designed for full frame, which is f/2 (so has a maximum eperture of 50mm diameter.) if we use that on a cropped body camera the aperture is still 50mm diameter, the 100mm lens focal lengh is still the same, as is the distance of the lens from the sensor. The only difference is that with the cropped sensor, we are just using the centre part of the potential image area the lens can produce, which has a zoom effect.
So the simple answer, the crop factor affects the focal length, not the aperture.