Roughly 1954 or 55 but you can find out for sure using the BARREL CODE letters stamped right in front of the action but on the barrel, same side as the serial number. and compariing them here for month and year. My 1950 is 108xxx so maybe yours could be 53 but no earlier. http://www.remingtonsociety.com/rsa/questions/barrelcodes Nice old guns.
Depends on the model.
Remington Works - 1914 (late)
your Remington model 6 was made in 1998,due to the S prefix on the serial#.
1912
1920
1924
1923
1912
1912
1917
1919
1913