Putnam County is the least extensive county in the U.S. state of Illinois. According to the 2020 census, it had a population of 5,637. The county seat is Hennepin. The county was formed in 1825 out of Fulton County and named after Israel Putnam, who was a general in the American Revolution. Putnam County is part of the Ottawa, IL Micropolitan Stat…Putnam County is the least extensive county in the U.S. state of Illinois. According to the 2020 census, it had a population of 5,637. The county seat is Hennepin. The county was formed in 1825 out of Fulton County and named after Israel Putnam, who was a general in the American Revolution. Putnam County is part of the Ottawa, IL Micropolitan Statistical Area.