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You need more info than the serial number. Date and month codes changed in about 1968.
Your serial number most likely was made in about 1958 to 1960 (Guess). My 760 is serial 337XXX and was mfg in 1960. You can go to the Remington Society web pages and identification process with charts are there.
The thing that changed in 1968 was firearms manufactures were required to put serials on even 22 lr many 22 rifles did not have them on it before then. The page is here:
http://remingtonsociety.com/rsa/questions/barrelcodes
(I put it there ;)
What else can I help you with?
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