A coupled-channel effective Lagrangian model respecting unitary and gauge invariance is applied to the combined analysis of (π, γ )N → K reactions for center-of-mass energies up to 2 GeV. The recent photoproduction data obtained by the CLAS, CBELSA, LEPS, and GRAAL groups are included into our calculations with the aim to extract the resonance couplings to the K state. Both resonances and background contributions are found to be important to reproduce correct shapes of the angular distributions and polarization observables. Our description of the data is of good quality. The extracted properties of isospin I = 3/2 resonances are discussed in detail while the I = 1/2 resonances are largely determined by the nonstrangeness channels.