They were made from 1890 to 1933, if it was made after 1920 (serial after 267K or so) there will be a barrel date code stamp on it. Check the Remington Society of America for a diagram and details. http://remingtonsociety.com/rsa/questions/barrelcodes
I can date some back to 1905 based on serial before that is a mystery ;) End of 1905 was 163884.
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