If you've got 
Particle CLI installed, I'd recommend this over the SmartConfig/App way.
Command: particle serial wifi
If you haven't you can also set the credentials via USB serial (for Windows you'd need to install drivers)
When doing it this way, you'd open a serial monitor (e.g. PuTTY) and enter w to get into WiFi credentials.
Important is that you should be asked about about your network security settings.
It does, but you can even have up to seven sets of WiFi credentials without problem, they'd just be scanned one after the other, if they fit to any of the present networks.
So there shouldn't be need to erase all existing credentials in order to get your Core connected to a new network (the oldest should get pushed out automatically)
But if you still find WiFi credentials after factory reset, you might not have performed it properly.
The Core needs to be flashing white rapidly for some time and come back into Listening Mode by itself.
BTW, there are some limitations for the CC3000
It can't connect to 5GHz networks, so deactivate this option on your router (b,g only)
It can't connect to WiFi channels >11, so set up your router accordingly.
See also
https://docs.particle.io/guide/getting-started/start/core/#prerequisites-for-setup