We use a full coupled-channels method to calculate collisional properties of magnetically or optically trapped ultracold 6Li. The magnetic-field dependence of the s-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at B=0.08T and B=1.98T. We show that the exact coupled-channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation.