this is so annoying. icloud.com NEVER remembers my browsers and always makes me two factor in

it has nothing to do with cookies / caches .

That is completely wrong. If you prevent your browser from saving cookies, or you remove them with a "cleaner", then Safari will ask you for a 2FID, 6 digit passcode every time you try to login here.

Hello, inck243!

From your post, it sounds like you are having issues with saving your Apple ID/iCloud login information on a trusted device and browser. We're glad that you reached out to the Apple Support Communities. We want to try and help you find the answers you need.

What type of computer are you using? Which version of the OS is on the computer? Does the computer show there are any OS or app updates available? If so, complete the updates to see if this corrects the issue.

Also, if you have not tried already, please restart the computer. Often this simple step will refresh the apps and software on the device to solve numerous problems you may encounter.

Another thing to try would be to clear the cache and history on your browser. Quit and close the browser app completely. Re-open the browser and check to see if this helps to resolve the problem.

We hope these steps help you out.

Warm wishes.

Did you disable cookies in your browser? If so, that would be why.

If you are using Apple ID created with secondary authentication and in your Mac you enter in the location system preferences , click on iCloud it will prompt to enter Apple ID and password , under security section you turn on 2FA .

An immediate mail will be received in your IMAP account , and you disable the 2FA within the time period of 14 days or immediately .

Again in system preferences - iCloud under keychain an error will be shown waiting for approval from other device having an exclamation mark .

And if you want to remove this error and again set up the iCloud Keychain and then plan to use your old secondary authentication Apple ID , see these steps .

( a ) Use an I phone and sign in with same Apple ID and password that is used in your Mac .

( b ) In your I phone go to settings - iCloud - open keychain - click on advanced two options will be shown .

Reset code and reset iCloud Keychain , so click on reset iCloud Keychain .

( c ) A verification code will appear on your mobile number through sms and it will prompt to generate a code , you have to think any desired number and fill up in the field , so keychain will set up in iPhone write down this code in a safe place .

( d ) Now come to your Mac and open system preferences , click on iCloud the box of keychain is unchecked , so tap the keychain box , it will show waiting for approval click on option button it will prompt to register with passcode enter the passcode that you generated in your iPhone and click on confirm .

( e ) Again in your iPhone device a pop up will appear showing approve or deny for your name and your Mac name say Mac book air or what ever Mac you are using and stating allow to approve for keychain , so click on allow .

( f ) So the waiting for approval from other device will be vanished .

( g ) In your Mac again click on option button in front of keychain , it will prompt to enter your trusted number an sms will come to your mobile having a verification code in it , so enter it your trusted mobile will be saved and visible .

Now , your iCloud keychain is set up from the server end and the Apple ID you are using is set with secondary authentication ( in which questions and answers for Apple ID are created ) and your 2FA is turned off .

Note : Suppose you have not followed this method for removing an error waiting for approval from other device and you think that erasing the hard drive and reinstalling the os or performing an archive installation , it will not help as this is the issue of iCloud Keychain from server end and not from your hardware of Mac .

Two factor authentication accounts are set with Mac , many users use private browsing permanently Use Private Browsing in Safari on Mac - Apple Support in which cookies are disabled , it has nothing to do with cookies / caches .

In the article Two-factor authentication for Apple ID - Apple Support

Once signed in, you won’t be asked for a verification code on that device again unless you sign out completely, erase the device, or need to change your password for security reasons. When you sign in on the web, you can choose to trust your browser, so you won’t be asked for a verification code the next time you sign in from that computer.

I turned on normal browsing in Mac .

Proof of nothing. The cookie already exists. You won't be prompted.

Cookies has no connection with 2 FA , even when I set private browsing mode the same procedure is followed to sign here for safari browser .

It absolutely does. I opened a new private window in Safari, and after entering my user password, it immediately prompted me for a 2FA 6 digit code, even though I was already logged in here in the browser window underneath.

But again, if Apple's cookie is missing, or intentionally removed, you will be prompted every single time.

Go ahead and try it. Open Safari's preferences. Under the Privacy tab, click the Manage Website Data button and remove the cookie, apple.com . Then try and login here again. You will get a 2FA prompt.

I turned on normal browsing in Mac .

It prompted to enter admin password , and didn't asked six digit verification code because the trusted number are verified in the account , at present the iPhone is not signed in same Apple ID and password as used in the Mac .

Cookies has no connection with 2 FA , even when I set private browsing mode the same procedure is followed to sign here for safari browser .

Deleted all web site data including apple.com cookies , it still prompted to enter admin password , no 6 digit code in safari browser , you might be using Firefox or other .

By the instructions I gave, it should be clear I'm using Safari.

fine , I am also using safari browser , it didn't promoted for code , if I click on cancel and follow upcoming steps the code option will appear , but not directly as I sign in .

Sorry, I have no idea what you mean by "directly". If you're logged out, the only way to sign in is to enter your user ID, which is then followed by entering your password.