The results of two searches for pair production of vector-like T or B quarks in fully hadronic final states are presented, using data from the CMS experiment at a center-of-mass energy of 13 TeV. The data were collected at the LHC during 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. A cut-based analysis specifically targets the bW decay mode of the T quark and allows for the reconstruction of the T quark candidates. In a second analysis, a multiclassification algorithm, the "boosted event shape tagger," is deployed to label candidate jets as originating from top quarks, and W, Z, and H. Candidate events are categorized according to the multiplicities of identified jets, and the scalar sum of all observed jet momenta is used to discriminate signal events from the quantum chromodynamics multijet background. Both analyses probe all possible branching fraction combinations of the T and B quarks and set limits at 95% confidence level on their masses, ranging from 740 to 1370 GeV. These results represent a significant improvement relative to existing searches in the fully hadronic final state.