Read here for more information on how Apple implements two-factor authentication:
Setting a device as trusted seems to be a waste of time; does it mean much or time out after a week or so?
Verification codes get send to one of your “trusted Apple devices”, or else to a “trusted phone number”.
The code itself is valid for a limited time, and usable one time.
Your trusted Apple devices would be Apple devices that are registered with your matching Apple ID account.
The trusted device stays trusted until you remove it from the list.
Manage your Apple ID - Apple﹥[sign in]﹥Sign-In and Security﹥Account Security﹥[edit trusted phone numbers and trusted devices as needed].
I don't know where Verification codes get sent if anywhere but I never receive them on my phone or e-mail;
On compatible Apple devices (iPhone, iPad, iPod touch, Mac), it would be a pop-up notification from the system software.
For phone numbers, it would standard be an SMS text message. I think a text-to-voice service option would also be available, if needed.
can't find any settings to nominate where the codes go; so every time I have searched for a code somewhere (forgetting that it never works) then ask for a text which arrives on the nominated phone.
If you have trusted Apple devices (all with the same Apple ID), then all of them would get a generic notification about the sign-in attempt. When confirmed on one of those devices, then the verification would show only on that device.
If you have trusted Apple devices, then a text message to the trusted phone wouldn’t be used initially.
If you previously had compatible Apple devices, that you do not have anymore now, then it may be time to clean up your list of trusted devices: Manage your Apple ID - Apple﹥[sign in]﹥Sign-In and Security﹥Account Security﹥[edit trusted phone numbers and trusted devices as needed].
