Here is my Babylonian-style base-60 multiplication table for 45.


I use commas to separate sexagesimal places. So 22,30 means 22 + 30/60, and 5,37,30 means 5 + 37/60 + 30/3600.


Sexagesimal Factorization: Base-60 Factor Pairs for 45

I found these five pairs that multiply to 45 (not using 1):


- 3 X 15 = 45

- 4 X 11,15 = 45  

  Check: 11,15 = 11 + 15/60 = 11.25, and 4 X 11.25 = 45

- 5 X 9 = 45

- 6 X 7,30 = 45  

  Check: 7,30 = 7 + 30/60 = 7.5, and 6 X 7.5 = 45

- 8 X 5,37,30 = 45  

  Check: 5,37,30 = 5 + 37/60 + 30/3600 = 5.625, and 8 X 5.625 = 45


So, including the example 2 X 22,30 = 45, there are at least six pairs that work. Three of my new pairs include base-60 fractions. This was a good way to practice thinking in base 60 and to see how fractions work in a sexagesimal place-value system.

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