Babylonian Numeration

Babylonians developed a base sixty numeration system. The basic symbols for 1 through 59 were additivley formed by repeating symbols. So base 60 means that the place values go 1, 60, 60 squared, 60 cubed etc. versus what we do now which is base 10. Their basic symols had different values depending on the position or location of the symbol. For example if we had 130 it would be 2(60) +10. Because the “tens” spot really represents the 60 squared.

A few more examples using ? representing 1 and > representing for 10.

??>>

This number would be 22

??   ?>  >>>

22(60 squared) + 12(60) + 3

This number would be  79,923

(Side note) I just wanted to let you know these are not the real Babylonian symbols. Thank you.

Greatest Common Factors

To find the Greatest Common Factor or GCF  are 2 types of factorization: prime factorization and listing factors. Among the common factors of two numbers there will always be the largest  factor which would be the GCF. Lets run through a couple examples and explain as we go.

1. Lets find the GCF of 12 and 36 using the listing method

The factors of 12 are: 1,2,3,4,6,12

The factors of 36 are:  1,2,3,4,6,9,12,18,36

Thus, the GCF of 12 and 36 is 12.

There are many special cases when finding the GCF could be, maybe the ONLY factor could be the greatest factor. Lets use the prime factorization method to find the GCF. The prime factorization method works best when using larger number.

2. Lets find the GCF of 360 and 72 using the prime factorization method

In any case there can and will be more  than one way to branch of and prime factor a number. However in the example as seen above you get the same ending result. 2x2x2x3x3x5

Next step is to factor 72 using the tree form

as you can see it is 2x2x2x3x3

Next step is to see what these to numbers have in common……. which is 2x2x2x3x3.

The final step is to multiply them together which is 72. So 72 is the GCF of 360 and 72.