The base-60 system is significant for several reasons. First, it's highly divisible, with more factors (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) than the base-10 system, making calculations involving fractions easier. This divisibility made it ideal for astronomical observations and calculations, areas where the Babylonians excelled. Today, remnants of this system persist in how we measure time (60 seconds in a minute, 60 minutes in an hour) and angles (360 degrees in a circle).