Friendship is a city in Crockett County, Tennessee. The population was 668 at the 2010 census. The city of Friendship was founded in 1853, …Friendship is a city in Crockett County, Tennessee. The population was 668 at the 2010 census. The city of Friendship was founded in 1853, though there was a post office in operation in the area as early as 1844. The city was plotted out in 1858, and incorporated the following year with W.P. Rice serving as the first mayor.
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