Q: how do i reset to factory settings a locked phone

Locked how? To the carrier?

iPhone: About unlocking

If by locked you mean the lock screen passcode, see the "Use Recovery Mode" section at the bottom of iOS: Forgot passcode or device disabled

If you mean Activation Lock (Apple ID) there is no way to reset or make the phone usable other than entering the correct password.

Open itunes, connect iphone, click restore