Alex Simons has recently blogged on "No password, phone sign in for Microsoft accounts". This a great enhancement in Microsoft second factor or "no password" technology.
There are a few things you need to consider to complete "phone sign" option.
If you have Microsoft Authenticator configured for your personal account, you will see an option from the dropdown menu to select Enable phone sign-in.
But you don't see this option If you are adding a new Microsoft account on an iPhone. Microsoft will automatically set it up for you by default. So add your Microsoft Account and login to a Microsoft service using this account. You will see an additional "password less" (use the Microsoft Authenticator app instead) sign in option as shown below:
If you don't configure or add your Microsoft account in your Authenticator App, you don't see a "use the Microsoft Authenticator app instead" option. Instead, you will have only see the password sign-in option as shown below:
You will see the following verification message on your login screen and on your mobile device.
If you are adding a new account on an Android device , It will be enabled by default and prompt you to complete it.