How do I save the maps that were downloaded from Offline Maps so that when I factory reset my phone I can simply put the backed up Offline Maps that were downloaded for reusing?
If your device is rooted, you can use Titanium Backup to backup the Maps application, which will backup the application and it's data.
After resetting, again install Titanium Backup, (you have to root again, if you had lost the root access, as a first step) and restore the Maps application. While restoring, you get a chance to opt for restoring app alone or app with data. When opting for the later, your offline data also comes.