Hi Carrie,
Identify your Apple TV model - Apple Support
If it was new in 2013, then it is most likely a 3rd generation (A1427 or A1469).
You can check its system software version in Settings. The last update was Apple TV Software 7.2.2 from December 2016.
If you have Two-Factor Authentication, and a device with older software, then the procedure is a bit special:
What if I use two-factor authentication on a device running older software?
If you use two-factor authentication with devices running older OS versions—like an Apple TV (2nd or 3rd generation)—you might be asked to add your six-digit verification code to the end of your password when signing in. Get your verification code from a trusted device running iOS 9 and later or OS X El Capitan and later, or have it sent to your trusted phone number. Then type your password followed by the six-digit verification code directly into the password field.
There is a time limit before the code expires, so request your code (or a new code!) after entering the characters of your password, to use those precious seconds effectively for just the code.
