The production of Z bosons associated with jets is measured in pp collisions at s=13TeV with data recorded with the CMS experiment at the LHC corresponding to an integrated luminosity of 36.3fb-1. The multiplicity of jets with transverse momentum pT>30GeV is measured for different regions of the Z boson's pT(Z), from lower than 10GeV to higher than 100GeV. The azimuthal correlation Δϕ between the Z boson and the leading jet, as well as the correlations between the two leading jets are measured in three regions of pT(Z). The measurements are compared with several predictions at leading and next-to-leading orders, interfaced with parton showers. Predictions based on transverse-momentum dependent parton distributions and corresponding parton showers give a good description of the measurement in the regions where multiple parton interactions and higher jet multiplicities are not important. The effects of multiple parton interactions are shown to be important to correctly describe the measured spectra in the low pT(Z) regions.