I have my phone number in my About area and the Facebook online search engine returns just my profile, so you know that's the best one.
Find Facebook Friends By Phone Number
However here's a search I did by phone number for someone I'm not connected to and who doesn't have their phone number in their public profile. (Sorry for the blurring-- to secure the innocent victim of my research.).
Ways To Hide Contact Information on Facebook.
1. Once again go to your account, click the [Accounts] tab and choose Personal privacy Settings link.
2. On the Personal privacy Settings page, scroll down and click on Customize settings link (see picture. above).
3. On the Customize settings page scroll to find Contact info section and it will reveal you all the contact information and whom you allow to see it.
4. Click on any among the contact info. like mobile number and choose the kind of people who can see/access it. If you wish to hide your contact number on facebook completely from everyone pick Customize. (see above).
5. In the next window under Make this visible to you can pick the option Just Me or the others.
Find Facebook Friends By Phone Number, By picking "Only Me" youre specifying that only you can see that contact information on your facebook profile, while the rest of the world won't see it at all or access from their phone book page, unless you define certain people in the above action to see them.