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Farnsworth is a census designated place in western Ochiltree County, Texas, United States. It lies at the intersection of State Highway 15 with FM376, southwest of the city of Perryton, the county seat of Ochiltree County. Its elevation is 2,995 feet (913 m). Although Farnsworth is unincorporated, it has a post office with the ZIP code of 79033. As of the 2020 census, Farnsworth had a population of 95.