  If a linear differential operator with rational function coefficients is
reducible, its factors may have coefficients with numerators and denominatorsof
very high degree. When the base field is $\mathbb C$, we give a completely
explicit bound for the degrees of the monic right factors in terms of the
degree and the order of the original operator, as well as the largest modulus
of the local exponents at all its singularities. As a consequence, if a
differential operator $L$ has rational function coefficients over a number
field, we get degree bounds for its monic right factors in terms of the degree,
the order and the height of $L$, and of the degree of the number field.
