I had this same problem, here'smy fix: I just got a new phone. Facebook had my prior carrier (Sprint) as well as my phone number saved, so FB thinks some other Carrier/App had hijacked my number now that it's on Verizon. Thankfully, I was already logged into facebook on my computer and/or older phone/tablet, so a notification there will arise asking if the new phone is really me. I confirmed it. On my computer, I also went into FB Settings, then Security, then removed my phone number, and then re-added it. I instantly got a SMS on my new phone, and a log in code. Perhaps you could try even logging in on your new phone before adding your number back in the Security section. I have re-enabled sms 2 factor authentication and things are fine now. (User reviews on Google Play store say do not use Google Authenticator since it is tied to your thumbprint stored on your phone and can be lost if your phone is ever lost).
