The serial number of a Browning firearm is usually found on the gun's receiver, but that location depends on the model number and make of the gun. Browning maintains a database of owner's manuals that can show gun owners exactly where the serial numbers are on their particular models.
The Belgium Browning is not a particular model of gun, as most Browning firearms have historically been manufactured in Belgium. Serial numbers help gun owners date their firearms, but they are not always reliable for older models. There are also several limited-edition models made by Browning that do not follow the company's traditional serial number pattern.