  We obtain asymptotic resolvent expansions at the threshold of the essential
spectrum for magnetic Schr\"odinger and Pauli operators in dimension three.
These operators are treated as perturbations of the Laplace operator in
$L^2(\mathbb{R}^3)$ and $L^2(\mathbb{R}^3;\mathbb{C}^2)$, respectively. The
main novelty of our approach is to show that the relative perturbations, which
are first order differential operators, can be factorized in suitably chosen
auxiliary spaces. This allows us to derive the desired asymptotic expansions of
the resolvents around zero. We then calculate their leading and sub-leading
terms explicitly. Analogous factorization schemes for more general
perturbations, including e.g.~finite rank perturbations, are discussed as well.
