This is also good for maintainability. Say you need to upgrade the algorithm but keep the old version around. You can create a new version of the algorithm specific parts without changing the public implementation and allow users to select which version to use; eventually changing the default. In a single class, this would be a nightmare.
"Nightmare" is a bit strong; that seems like a very normal and straightforward refactoring step... iff you avoided putting the low-level stuff into your public API.
