The National Archives of the United Kingdom makes available a very helpful tool for free on this site. It's DROID - Digital Record Object IDentification. (I love a good acronym.) It can be used to correctly determine the file format of digital files when the files' extensions are absent or missing.
In this example I have a small set of files. The extensions for these files are all either incorrect or simply missing.
After downloading the zip file containing the DROID files, if you are using Windows you should click on the file named, 'droid.bat'. This will open the application.
Use the plus sign on the tool bar to add the files you want to analyze.
DROID quickly detects the correct format of the files.