We present measurements of the differential cross section and Λ recoil polarization for the γp→K+Λ reaction made using the CLAS detector at Jefferson Lab. These measurements cover the center-of-mass energy range from 1.62 to 2.84 GeV and a wide range of center-of-mass K+ production angles. Independent analyses were performed using the K+pπ− and K+p (missing π−) final-state topologies; results from these analyses were found to exhibit good agreement. These differential-cross-section measurements show excellent agreement with previous CLAS and LEPS results and offer increased precision and a 300-MeV increase in energy coverage. The recoil polarization data agree well with previous results and offer a large increase in precision and a 500-MeV extension in energy range. The increased center-of-mass energy range that these data represent will allow for independent study of nonresonant K+Λ photoproduction mechanisms at all production angles.