  We introduce the F-adjoined Gauss map. We use it to express the Gaussian
maximum likelihood degree as a product of two invariants. As an application of
our product formula, we classify all projective curves of Gaussian maximum
likelihood degree 1. We also provide a formula for the generic Gaussian maximum
likelihood degree of a projective variety $X$ in terms of its polar classes.
The renowned polar class formula for generic Euclidean distance degree is a
special case of our formula.
