Essentially first year production 1922 (they made just a couple in 1921) it will also be date code stamped, see related links.
Your Remington model 1903 was made in the year 1941,with the serial number that you have provided.
Your remington model 700 which has a letter A prefix to the serial number,indicates that it was made in 1980.
With the serial number that you provided,your Remington Rand made 1911-A1 was made in the year 1945.
1918
1920
The C prefix to your serial number indicates that your remington model 700 was made in either 1982,or 2008.
1909
Made 1909 to 1936
1926
1987
1910
Impossilbe to answer without a serial number.