Unknown file type containing a virus
File extensions tend to be present only as mnemonics for the user to quickly identify a file, and for software to filter out incompatible files prior to loading and opening them. The latter explains why your OS did not recognize the file type.

To execute a file is common lingo, even if inexact: you execute a program, which then tries to parse the file. Should this program fail to parse the file, it will either report the error or crash. This means that you're probably safe.

Second, Android employs a deal of security mechanisms in order to limit the execution of possibly malicious software. For example, malware tend to come in the form of binary files. On modern Android versions, such files (as well as plaintext scripts) cannot be launched from neither the internal or the external storage (if any). This means, that the only kind of file that could harm your device are APK files that have been installed – namely, apps.

Even then, apps are restricted in many a way, as each of them run in an isolated context, being able to communicate with others only via predefined means. Therefore, the only way some code could do harm to your device, is if the operating system itself presents bugs that can be exploited, and such issues stem from OSes that haven't been updated in a while. Indeed, even other apps could be exploitable, but for an attacker to make use of such a weakness, they would need prior knowledge of your installed software (and even then, they could only gain access to what the vulnerable app itself can access).

If I were you, rather than worrying about having been infected, I would be concerned about my browser downloading files without my expressed authorization. You needn't do a factory reset, but you may want to replace your browser if it continues in its behavior.