How do vigesimal number systems work in Mesoamerican languages?

Vigesimal number systems, which are based on combinations of 20, are a defining structural trait shared by essentially all Indigenous languages of Mesoamerica.

In these systems, counting proceeds in multiples of 20. For example, in the Mayan language Chol, the system functions as follows:
* hun-k’al: 20 (1 × 20)
* cha’-k’al: 40 (2 × 20)
* ush-k’al: 60 (3 × 20)
* ho’-k’al: 100 (5 × 20)
* hun-bahk’: 400 (1 × 400)
* cha’-bahk’: 800 (2 × 400)1

While the base is 20, some systems were modified for specific purposes, such as timekeeping. The Maya, for instance, used a vigesimal place-value system but substituted 18 for 20 as the multiplier for the second order of units. This resulted in a tun (a unit of 360 days) rather than 400, which helped track the 365-day year more closely. Similarly, the Cakchiquel of highland Guatemala utilized a vigesimal system where the counting unit was the a (400 days), with may representing 8,000 days (20 × 400).23

These systems reflect a sophisticated approach to mathematics and chronology that allowed Mesoamerican civilizations to record complex historical and astronomical data.32