Can't get friends icloud account off of my phone?

I let my friend borrow my IPhone 6 and she logged out of my icloud and logged into her own but afterwards she forgot ALL the info to her icloud. Password, email, security answers and all. We tried to factory reset the phone and it worked but the icloud account is still on there when we power the phone up and we have to log in to get any further than choosing a language.

Your best bet is to have your friend get access to the e-mail associated with her icloud account to be able to reset the password. Otherwise your phone is not worth much more than a brick, and your friend should be buying you a new phone.