If you're going to perform a factory reset on your phone, don't change your Google account password. Thanks to a new security feature Google's adding to the newest versions of Android, changing your password right before resetting your device will trigger an irreversible 72-hour lockout on your device.
As of Android 5.1 (or earlier, depending on your OEM), Android comes with some built-in device protection features that help keep your phone safe in the event of theft. One of these features, Factory Reset Protection, requires you to sign into the phone with the Google account you previously used to log in. The idea here is, if a thief steals your phone, then immediately resets it, they won't actually be able to use it unless they also have your account login information.
"Well, what's to stop a thief from resetting my password themselves and using that to log in to my phone?" Good question! Since your phone can receive your two-factor codes and emails, getting access to your phone makes it pretty easy to reset your password. For that reason, if someone changes the password on your Google account and then immediately resets your phone, Google assumes a thief has your device and begins a 72-hour lockout.
The idea of the lockout is that it gives you time to retrieve your phone if it's been stolen before a thief can access it. In the event that you really do need to do a factory reset on your phone and change your password, there's a simple solution: do the factory reset first. Once you've logged into your new device, you can change your password just fine. Alternatively (and this is likely even more safe): change your password, then wait at least three days before resetting your phone.
As Android Police also notes, if you're resetting your device to sell, you'll need to manually disable the lock screen and remove your Google account entirely. Not only is this one more reason you should lock your screen, but doing so will prevent the device from requiring an account sign-in after a reset.