Harding County is a county in the U.S. state of New Mexico. As of the 2020 census, the population was 657, making it the least populous county in the state, and the 13th-smallest county by population in the United States. Its county seat is Mosquero. The county is named for United States President Warren G. Harding, and was created on the day of his inauguration as president on March 4, 1921, making him the most recent president to have a county in any state named after him.

Union County is the northeasternmost county in the U.S. state of New Mexico. As of the 2020 census, the population was 4,079, making it the fourth-least populous county in New Mexico. Its county seat is Clayton. The county was formed in 1894. Union County borders Colorado to the north, and Oklahoma and Texas to the east.