Sexagesimal Number System

Sexagesimal, also known as base 60, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.

This is also why certain French dialects say numbers between seventy and seventy-nine as their relation to sixty. E.g. soixante-douze (sixty-twelve) is 72 , and soixante-dix-neuf (sixty-ten-nine) is 79. It's not "certain French dialects", it's just French ! And i think this explanation is wrong, the origin I heard is that originally, we used a base-20 system : 30 was vingt-dix (twenty-ten), just like our 70 of today. And we still use quatre-vingt (four-twenty) for 80, because it's 4x20. Thus, 99 is said "quatre-vingt-dix-neuf" (four-twenty-ten-nine).

​The most common system of counting today uses the number 10 as its base. In this system numbers are packaged in units of 10; two tens are 20, three tens are 30 and so on. This numerical base is as ancient as the need for humans to count and probably comes from our 10 fingers which, before the days of writing would be the easiest method to count.

Less obvious is the reason for using the number 60, a number still widely used today with 60 seconds in a minute, 60 minutes in an hour, 60 minutes of arc in one degree of angle and six times that number of degrees, 360, in a circle.

The number 60, a superior highly composite number, has twelve divisors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6.

The most powerful driver for rigorous, fully self-consistent use of sexagesimal has always been its mathematical advantages for writing and calculating fractions. In ancient texts this shows up in the fact that sexagesimal is used most uniformly and consistently in mathematical tables of data. Another practical factor that helped expand the use of sexagesimal in the past, even if less consistently than in mathematical tables, was its decided advantages to merchants and buyers for making everyday financial transactions easier when they involved bargaining for and dividing up larger quantities of goods. In the late 3rd millennium BC, Sumerian/Akkadian units of weight included the kakkaru (talent, approximately 30 kg) divided into 60 manû (mina), which was further subdivided into 60 šiqlu (shekel); the descendants of these units persisted for millennia, though the Greeks later coerced this relationship into the more base-10–compatible ratio of a shekel being one 50th of a mina.