I recently use 2-step verification to sign-in my Google account.
But after turning this on, I cannot sign-in my phone since no SMS is sent to my phone.
What can I do to sign in now?
If you signed up for 2-step verification, you may need to enter an application-specific password in place of your regular account password. You can generate an application-specific password when you are authorizing access to your Google Account. This process takes a few minutes, and you only need to do it once per application or device.
Note: For Android devices running 4.0 or higher, you do not need an application-specific password and only need to submit your username and password. You'll be directed to another page where you can enter a one-time six-digit code.
To check if 2-step verification is on or off, visit https://www.google.com/settings/.
I had a hard time because I had two Gmail accounts on my Android,: one for work and one personal. The process is broken if you have two accounts and you try to apply two step auth on a phone (I have a Galaxy 4 by Samsung).
The solution was to delete my personal account off the phone, do the sign-in process which kicks out an SMS 6-digit code then authenticate (worked). Afterwards you can add back the second account.
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