I believe that your Sears shotgun is a Winchester model 37A shotgun that was made for Sears Roebuck And Co,.
what is the age of a browning ranger repeating 12 ga shotgun serial number 45579 b
Check the barrel and receiver.
The Sears Roebuck Model 20 12 gauge shotgun, serial number 5832006 is valued at $200 in very good condition. It good condition, it is valued at $125.
1936. I have my fathers 16 gauge Ranger Sears and Roebuck Co. U.S.A now that he has passed on. He got it new in October of 1936 for his 16th birthday. Seral # 4991.
Can't answer without knowing if it is a rifle or shotgun.
100-300 USD. http://www.e-gunparts.com/crossref.asp
No published sn data.