Farnum was born in Saginaw, Michigan and raised in a farm community at Watrousville. He graduated from Vassar High School, Vassar, Michigan, in 1933 and continued his education in the Civilian Conservation Corps, 1933-1935. He took special educational courses and was employed in the motorcar industry in Pontiac, 1936-1952. He engaged in union activities ranging from shop steward to international representative for United Auto Workers-Congress of Industrial Organizations, 1942-1952. He was administrative aide to U.S. Senator Blair Moody, 1952–1954 and assistant Michigan Secretary of State, 1955–1957; deputy Michigan Secretary of State, 1957–1960; and Michigan Auditor General, 1961-1965. He was a delegate to the Democratic National Conventions of 1956, 1960, and 1964.