How did the Babylonian sexagesimal system use base 60?

The Babylonian sexagesimal system was a positional numeral system that utilized 60 as its base. Because 60 is a large base, the Babylonians did not use 60 unique symbols for the digits 0 through 59; instead, they employed a simple additive decimal (base-10) grouping system to represent these values. For instance, symbols for 1 and 10 were combined to form numbers from 1 to 59.12

To express larger values, the Babylonians applied the concept of place value, where the position of a digit indicated the power of 60 it represented. For example, a symbol could represent 1, 60, or ${60}^2$ depending on its placement. This system was highly effective for division because 60 has many divisors (2, 3, 4, and 5), which facilitated calculations.12

However, the system faced challenges due to the lack of a consistent placeholder for zero, often requiring context to determine the intended power of 60. This sexagesimal method eventually influenced mathematical astronomy, and its legacy persists today in the use of minutes and seconds for measuring time and angles.123