  Factorization underpins our ability to make predictions at the LHC, both in
Monte Carlo simulations and direct calculations. An improved theoretical
understanding of jet substructure can lead to calculations that can confront
data and validate the Monte Carlo description of jets. We derive constraints on
jet substructure algorithms from factorization, focusing on the broad class of
jet observables where the soft and collinear dynamics of QCD dominate. A
necessary condition for factorization is that the phase space constraints on
soft and collinear dynamics for a given observable are independent of each
other. This condition allows us to use a simple power counting analysis to
place strong constraints on the form of jet substructure methods that can
factorize. We illustrate this approach by considering four substructure
algorithms, the mass-drop filter Higgs tagger, pruning, trimming, and
N-subjettiness. We find that factorization constrains the scaling of parameters
in all of the substructure algorithms, and that the generic declustering and
filtering techniques do not factorize. However, we determine simple
modifications that can be made to allow for factorization.
