It depends on the model. The numbers are always on the receiver, never the barrel. Pumps and autos are on the bottom of the receiver, forward of the carrier. Over/Under serial numbers are under the action release lever on top of the tang. Move the lever to open and you will see the serial number.
A Browning Auto 5 Lightweight shotgun was made in 1957 with that serial number on it.
1977
No serial number provided
It was made in 1965
You must call Browning with the serial number to find out.
1966
Impossible to answer without a serial number and detailed description.
Receiver
This gun was made in 1960
Possibly if it is a Browning made by Miroku.
The letters MW in the serial number of your browning stand for the year of manufacture which was 2004.
No way to answer- the serial number does not tell us what the gun IS. Please repost with a description of the gun, caliber/ gauge, and condition, and we can give it a shot.