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The old factory ledger, available on this web site, begins in September 1919, at serial number 199611 for the 12-gauge Model 11 autoloaders, about the time the company resumed civilian production after the Great War. So, your gun was likely made in the mid-teens. Remington Arms Co. introduced the John M. Browning designed Remington Autoloading Gun in 1905.
In 1911 the company name was changed to Remington Arms - Union Metallic Cartridge Co., and about that time they began referring to the autoloading shotgun as the Model No. 11. In 1920, the company name was changed again to Remington Arms Co., Inc.