There are 4 US Post Offices in Dent County serving a total of 15,082 residents equating to 3,771 residents per post office. It's estimated that approximately 24,073 packages are handled across the 4 county post offices annually. Dent County is a county located in the U.S. state of Missouri. As of the 2010 census, the population was 15,657. The largest city and county seat is Salem. The county was officially organized on February 10, 1851 by Dustin Counts & Nicholas Berardy, and is named after state representative Lewis Dent, a pioneer settler who arrived in Missouri from Virginia in 1835.