A system of counting using a base of 60 rather than 10.

The number 60 was used as a base for counting by the ancient Sumerians and the cultures that followed them, the Assyrians and Babylonians. I have heard or read of a few theories as to why:

• The year has about 360 days.
• A basic unit of coinage, the mana, was divided into 60 shekels, and counting followed accounting.
• 60 has a lot of convenient factors, and the priestly classes who did the counting adopted the system to avoid inventing fractions.
The Babylonians actually used a sexagesimal positional notation for writing numbers; there were 59 patterns of two basic cuneiform marks. This system had the unfortunate flaw of lacking a symbol for zero, meaning that certain renderings could be interpreted as several different numbers. Just think what it would be like if "37" could be interpreted as 37, 307, or 370. Around 2000 BCE they began to catch on to this and began putting spaces in numbers where we would today put zeroes. In about the 300s BCE some Babylonian scribes began using a special "zero" symbol instead of a space.

The remnants of Babylonian sexigesimal numbers are still around today:

• Hours are divided into 60 minutes, which are divided into 60 seconds each.
• Angles are measured in degrees, 360 of which make a full circle. Degrees are also divided into minutes and seconds.