With the factory reset process completed, your iPhone should reboot and show you the first setup screen. At this point, you shouldn't do anything else with your old iPhone. If everything has gone right, your old iPhone only has the iOS and built-in apps on it and is ready for its new owner to set it up.
The best way to confirm that this is the case is iCloud and Find My iPhone. Log in to Find My iPhone at https://www.icloud.com/#find. When you've logged in, check to see if Find My iPhone shows your old phone. If it doesn't, you're all set to move to the next step.
If your old phone still shows up in Find My iPhone, use the site to Erase your iPhone. When that's done, select your iPhone and remove it from your account. If you don't do this, your iPhone will still be locked to your Find My iPhone account and the new owner won't be able to use it — and no one likes an unhappy buyer.