Count the number of grooves.
Remington used a four groove barrel at the start of production. The Ordnance Dept approved the two groove barrels in Oct 1942. Remington had switched over to the simpler to manufacturer two groove by early 1943. Both two and four groove were used concurrently after that point.
The Smith-Corona A3's used two, four and six groove barrels from two different manufacturers, High Standard and Savage (through HS).