physical chemistry - What are the units of Kc and Kp?

They are both equilibrium constants as far as I know.
Kc is in terms of molarity and Kp is in terms of pressure. Also both of them are ratios of respective quantities [ ratio of molarity(s) in Kc and ratio of pressure(s) in Kp], so they should be dimensionless according to dimensional analysis. But in some places I have seen units mentioned along with both Kc and Kp. It is quite confusing and I don't see any uniformity in this. Anyone please help.