Do I have to use the core factor to license SQL Server 2014 and prior versions in SPLA?

No, the core factor was intended to level the playing field between Intel processors and AMD processors at the time of SQL Server 2012 (when Microsoft changed the SQL processor licenses to SQL core licenses). If your servers have single core and dual core processors the core factor sets a 4 core minimum for physical processors.

If your AMD processors have more than 4 cores, the core factor allows a maximum 4 core licenses for the AMD processors shown on the table (instead of the actual number of cores which may be higher). With the introduction of SQL Server 2016, core factors have been removed from licensing.