Actually there is crop factor:Maybe because it would be the equivalent of much more mm (actually 640) on a 1.6x crop body and some need it?EF-S 400 4 IS
Why not try the EF 300mm f/4L IS, as it is the equivalent of 480mm on a 1.6x crop body?
No, a theoretical EF-S 400mm lens on a 1.6x crop body would be the equivalent of 400mm. Note: EF-S lenses, which is what the OP requested, can only be mounted on a 1.6x crop body, so there is no crop factor.
EF-S10-22 gives the equivalent of 16-35 for example.
The difference is that EF-S lenses cannot be used on full frame and there is no spare glass in the sense that the imaging circle is not big enough for full frame. So the quality may (or may not depending on the lens) suffer at the very edges.