  We consider the Hurwitz action on quasipositive factorizations of 3-braids.
We prove that every orbit contains an element of a special form. This fact
provides an algorithm of finding representatives of every orbit for a given
braid. We prove also that (1) any 3-braid has a finite number of orbits; (2) a
Birman-Ko-Lee positive 3-braid has a single orbit; (3) a 3-braid of algebraic
length two has at most two orbits.
