This tutorial in which you learn how to disable Apple ID Two-Factor Authentication, it is still current only for those who have this security feature activated for less than two weeks. Apple no longer allows the option to disable Two-Factor Authentication for Apple ID. In addition, accounts that do not activate two factors authentication cannot access Apple services that involve a high level of security.
Initial article.
CAREFUL! Disabling the two -factors authentication option can make your Apple account available to badly intentional third parties. It can lead to the loss of personal data, paid applications and even money, if you have a bank account or use the Apple Pay!
Many users find it useful additional security measure For Apple account (iCloud / Apple ID). Authentication with two factors (Two-Factor Authentication), it's one plus security For the Apple account when we first log on with it on a device or a web browser.
This process implies generating a six -digit account, trimis pe un device (iPhone, iPad, MacBook) already authenticated. Code to be confirmed on the new device. If we do not hold an Apple device but we account for iCloud, The six -digit code will be sent on a phone number which we considered to be confident and added when I created the iCloud account.
This way, even if a badly intended person finds us the password of iCloud, cannot access the account without this code that is sent automatically after a correct authentication.
Some users do not consider this additional security method necessary. Ask for little additional time for authentication to the usual method, and what is the most stressful, some applications that we want to connect our email address iCloud, I do not recognize the authentication process. I met this problem recently, on the Email application of Windows 10, which does not allow me to authenticate Two-factor for the iCloud address.
How do you disable Apple ID Two-Factor Authentication
If you are determined to give up this security method, you can turn off Apple ID Two-Factor Authentication, following the steps below:
1. Access from Mac / PC Web address:appleid.apple.com Where do you authenticate with your Apple ID and here you will ask you to enter the 6-digit code.
2. At the section Security, click on the link “Edit” from the right side.

3. At the Security settings, at the bottom-right, we click on the link “Turn Off Two-Factor Authentication“.

4. Click on confirmation “Turn Off Two-Factor Authentication“.

5. Set three answers to three security questions for Apple's account, then check that the email recovery address is correct. After completing these steps, the TWO-Factor authentication will be deactivated.

This way, you managed to disable Apple ID Two-Factor Authentication. After deactivation, you will be automatically disturbed from all the applications and browsers you have authenticated account of iCloud. Including from iPhone, MacBook or iPad.
Later edit.
IPhone owners who use the application iMessage they will have to reactivate this service. The cost of activating the IMESSAGE service is the equivalent of the value of sending a SMS international.
It will work
Will it work on a Mac with OS10.9.5 system or if I should make an update?
Of course. without problems, everything will be normal.