The results reported in this paper come from a K-p-formation experiment performed in the Argonne-Michigan 40-in. heavy-liquid bubble chamber. About 500 000 pictures were taken in a mixture of 80% propane (C3H8) and 20% Freon (C F3Br) with K- beam momenta between 730 and 900 MeV/c. Cross sections for the pure isospin states Σ0π0, Λ0π0π0, and Σ0π0π0 in the center-of-mass energy ranging from 1580 to 1720 MeV were measured. Cross-section measurements of the Λ0π0, Λ0η0, Λ0π+π-, and Σ0π+π- final states were compared with previous data obtained using hydrogen bubble chambers to check the validity of our techniques. The cross-section normalization was performed using τ decays to determine the kaon flux. The angular distributions for Λ0π0 and Σ0π0 are also presented and compared with previous measurements in hydrogen bubble chambers. A check of the technique used previously in hydrogen-bubble-chamber experiments to obtain the Σ0π0 angular distributions suggests some contamination in the hydrogen data from the multiple π0 final states. Our data are consistent with the Λ0π0π0 final state being produced almost entirely through Σ(1385)π, and the Σ0π0π0 data with almost total Λ(1405)π production.