If you are looking for a free word processor for your mobile device, you might want to try Quip. The app is currently only available in iOS, but you can sign up for a preview version of the Android app.
The feature packed app includes a suite of tools for collaborative editing, including a way to chat with your co-writers while writing together in virtual space. Unlike many mobile writing programs, Quip also tracks your changes in a document. Check it out:
Diffs are simple visual representations of edits to a document. Diffs get added to the thread every time an edit is made, showing what’s changed, who made the change, and when they made it. When someone else edits a document, diffs make it easy to stay up-to-date without re-reading the whole document.