There is a couple of hardware/software independent data points: time zone, currency, locale.
And if every option cuts the user base in half, becoming unque is a matter of 33 such options.
The fingerprint is comprised of more than device and OS:
Browser type and version
Screen resolution
Installed fonts
Browser plugins and extensions
Canvas fingerprinting data
WebGL (graphics hardware info)
Time zone
Language settings
IP address
HTTP headers
Touch support
Device type
AudioContext
My iPhone is allegedly unique to 1 in 2,147,483,648+ devices.
But I wonder how true that is, given how many people use the same model and iOS version as me.