To resolve this concern, user should ensure that the code looks correct and the most recent one shown in your authenticator app. This authenticator app relies entirely on the time set on your device to create the code. In case the time on mobile does not match with the time on your computer, then code will not work, and that's when Facebook two factor authentication not working issue arises.
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If you're having trouble adding or using your security key, make sure that you have set up either text message (SMS) codes or a third-party authentication app first. If you have already set up one of those two security methods, try clearing your cache and temporary data.