This paper develops the theory of factorial numbers formed by positional number systems with mixed-base factorial number systems. The fundamentals of the theory of factorial numbers are outlined. a method for obtaining them is given. their range is determined. https://www.roneverhart.com/HP-Chromebook-X360-14b-ca0013dx-14-HD-Touchscreen-1366-x-768-Laptop-Intel-Celeron-N4000-4-GB-RAM-32-GB-eMMC-Intel-UHD/