You will need to enable SYNC with your Google account, given the contacts are still there.

Open your Gmail account, make sure your contacts are intact. If you see them, then go to System Settings - Accounts tab - Google, touch the email address listed on top of the screen. Once you open details of your sync Google account, check the Contacts box and your phone should sync them in manner of minutes.

Make sure your SYNC in enabled in your notification. Pull down the notification on top of your display, and select the SYNC. If Sync is not listed, press the little 4 tiles icons like, in the top right corner, to view all your activities within the Notification area.

 

If you added them normally as a Google contact, they should be in there. When you factory reset and the phone reboots it should then ask you to log in to your Google account. Once the setup is finished it should auto sync (sync should auto enable) and grab all of your contacts.

Go into your Settings > Accounts > Google and tap on the little sync icon. You should see a large list of things to sync. Be sure to untick anything you do not need synced (like Google Photos if you do not use the service).