To increase my understanding, I found two good theories as to why a sexagecimal number system would have been chosen. The first theory is that it would have been a combination of two number systems from different tribes, such as base 5 and base 12 or base 6 and base 10. The resulting base 60 would have been useful for the tribes who trade between each other. Some evidence points to the combination of base 6 and base 10 to be more likely because of the way ones and tens were used to create unique symbols for numbers. Another common theory is that 60 was chosen for its prime factorization (2x2x3x5) and versatility, since it's the smallest positive integer whose factors include all numbers from 1-6, and it is also divisible by 10, 12, 15, 20, and 30.
Another part of their number system that I found to be rather interesting is the fact that they had no radix point and they had no symbol for zero for the first 1000 years. While this seems like this would make it very hard to distinguish numbers, they simply used the context to determine the exact number. An example of this issue is the number 1 21 ([1x60]+21), which equals 81 but can also mean the reciprocal of 81 or 1/81. You would have to understand the context in order to know which number it actually was. The lack of a zero symbol created the same issue. While it would make sense to write 3615 as 1 0 15 ([1x60^2]+[0x60]+15), it was written as 1 15 which also can equal 75 ([1x60^2]+15 or [1x60]+15). Again, context makes a huge difference. Even though these issues seem like they would result in a lot of errors, there is little evidence that the Babylonians struggled with them.
While their number system is very different from ours and may seem more difficult to use, I do understand some advantages it may have and see that it was fairly advanced for its time.
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