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Clean the Touch ID sensor
If your MacBook, iPad or iPhone touch ID doesn't respond, it is possible that the Touch ID sensor is dirty and it can't recognize your fingerprint. Grab a piece of soft cloth, gently clean the sensor and try again.
Maybe the Touch ID works perfectly but it doesn't recognize your fingerprint because you are using the wrong finger. Every finger on our hands has a different fingerprint pattern so, if you used your thumb when setting up the Touch ID, the Touch ID sensor will recognize only the thumb.
Note: If you want, you may save up to 5 fingerprint patterns in your device, in Settings -> Touch ID & Passcode.
Maybe the Touch ID doesn't work because your device "forgot" your fingerprint pattern. In order to fix this and make the Touch ID sensor recognize your fingerprint pattern again, you will have to "retrain" it.
To retrain your device, follow the steps below:
Go to Settings -> Touch ID & Passcode;
Enter your passcode, tap on a fingerprint pattern and tap on Delete Fingerprint; *Delete all the fingerprint patterns if you have more than one, to make way for new ones;
Tap on Add a Fingerprint... and follow the on-screen instructions;
Feel free to watch the video below if you are not entirely sure on how to add fingerprint patterns:
Note: Ensure to wipe the Touch ID sensor before "training" it.