It depends on the authenticator app you choose. Both the Google Authenticator and RapidIdentity apps that run on your mobile device use a time-based one-time password (TOTP) algorithm to provide a valid 6-digit code (it is not texted to your phone). So while the application RUNS on your phone, you are not sharing the number with anyone, nor being changed any fees. However, other authentication vendors may required you to enter your phone number when registering for the application.
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