Now is a good time to enable two-factor authentication on your accounts. Here is how to do so for some common services: - Google: https://www.google.com/landing/2step/ - Github: https://github.com/settings/security - AWS: http://aws.amazon.com/mfa/virtual_mfa_applications - Facebook: https://www.facebook.com/settings?tab=security - Twitter: https://twitter.com/settings/security - Dropbox: https://www.dropbox.com/acco…
With two-factor authentication you are happily providing gmail with your phone number. They say they need this to send you a verification code when you log into your gmail account. Then they say: "During sign-in, you can tell us not to ask for a code again on that particular computer." Well, if that's the trick, they don't need your phone nr at all, they can do ip and os check anyways..
The goal of 2FA/MFA is to make you demonstrate that you're in possession of two independent secrets (authentication factors). Once you've shown that, it's considered safe enough to replace the second secret (OTP sent to your phone or generated by your TOTP app like Google Authenticator) with a cookie (the check is not IP-based). Typically the cookie only lasts for 30 or 60 days.
If what you're concerned about is the idea that Google knows your phone number, you can use Google Authenticator or another TOTP app instead.