It's actually Sumerian. They taught the Akkadians everything. The Babylonians and Assyrians are descendants of the Akkadians. So they used base-60 because you can divide it with 2, 3 and 5. (Base 10 can only be divided with 2 and 5.) Base 60 was also used because they used fractions not decimals. They used the abacus to do addition and subtraction. The earliest versions were pebbles in a sandbox.
So fold your left thumb over your left palm. With your right thumb, you count the exposed knuckles of you left hand from 1 to 12. With your right index 13 to 24. Count from 25 to 36 with your middle/ salutary finger. With the ring finger 37 to 48. And with the pinkie finger 49 to 60.
The Sumerians divided the night sky into 360 degrees. Here's where divisions come into play. So they were an agricultural society. They needed to know exactly when to plant crops. They thought that the Sun revolved around the Earth. The Earth in reality spins on its axis which c. 23 degrees from the “path” of the sun across the sky ie plane of the ecliptic. The Sumerians noticed where those lines intersected after winter. That's the spring equinox. So divide 360 by 2 you get 180. That's the fall equinox. Divide 360 by 4 you'll get 90 that's the summer solstice. 270 is the winter solstice.
Now divide 360 by 12 and you get 30. They noticed certain patterns with stars on the sky. So on the plane of the ecliptic they noticed 12 shapes. These became the 12 constellations of the zodiac. Each one occupied 30 degrees of the sky. That's how they knew where the sun would rise during the spring equinox.
They also noticed a phenomenon whenever a solar eclipse occurs. The moon is almost the same size as the sun during certain eclipses. They occupy half a degree of the sky.
On earth, 90 degrees was the North Pole and 360 degrees was the equator. (The zero was still in India. The prime meridian of longitude won't be decided until the 1885 Berlin Conference.) Degrees of angles and coordinates are divided into 60 minutes each and minutes into 60 seconds each because of this.
The Sumerians started the day on sunset of the previous day. The nighttime was divided into 12 hours regardless of season or latitude. So 12 divided by 2 is midnight or as they called it the sixth hour. The daylight time was also divided into 12. Hence the siesta in Spanish speaking countries. Hours were also divided into base 60 minutes and seconds. Thus the Sumerians also invented the sundial.
So the Babylonians learned this from the Sumerians. The exiled Jews, the Persians and the Greeks after Alexander the Great conquered Persia in 330 BC learned from the Babylonians. The Romans learned from the Greeks.
Footnote #1: The Greek astronomer Hipparchus discovered the precession of the equinoxes. It's 26k year cycle. 1AD (there's no 0AD) was the start of the Age of Pisces. So 26000 divided by 12 is 2166 AD. That's when the Age of Aquarius will start.
Footnote #2: The Babylonians after 700 BC discovered the 19 year Metonic cycle. Every year was calculated to have 365.26 days. Meton introduced it to the city of Athens after 500 BC. Caesar used the 76 year Callippic cycle where every year had 365.25 days. Hence the origin of leap days.