How to disable Apple’s Two-Factor Authentication for macOS?
Older Macs do not support Two-Factor Authentication. As a side-effect, a user cannot access their iTunes account in iTunes on any older Mac, and cannot buy music.
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Two-Factor Authentication is applied at the account level, not at the device level. So you can either remove it entirely from your iCloud account, or you’ll have to use it on all of your devices equally.
If it worked any other way a hacker could simply pick the least secure entry point to attack your account.
Thankfully you can still login on an older device, even with Two-Factor Authentication enabled.
First, login using your regular credentials, just as you would on a system that did support Two-Factor Authentication. An authentication code will be sent to all your Trusted Devices. Now simply login again, this time appending your authentication code to your password.
For instance if your account is [email protected], your password 123apple and your authentication code 456789, then you would login using the following credentials:
[email protected] 123apple456789
You can read up more about this at Two-factor authentication for Apple ID:
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, 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.
Apple also provides a few additional methods to Get a verification code and sign in with two-factor authentication.