Please check the link for the Manufacture Date codes details on the Remington Society of America.
Lookup date code on Remington Society of America here: http://remingtonsociety.com/rsa/questions/barrelcodes
By the serial number and markings on the barrel.
To determine the age of a Remington Model Sportsman with the serial number 773769, you would typically refer to Remington's serial number lookup resources or historical production records. The Model Sportsman was produced from 1939 to 1962, so the serial number indicates that it was likely manufactured in the early 1950s. For an exact year, consulting a detailed Remington reference guide or contacting Remington directly would provide the most accurate information.
Remington's website has a history section that you can look at.
The value of a 20 gauge Remington Sportsman 58 would actually depend on a number of things. A couple of those things would be the age and condition.
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