math

About

Base-12, also known as Duodecimal or Dozenal is a positional number system that utilises 12 as the base radix and has 12 symbols that consist of 0-9 and two more commonly denoted as "A" and "B", this base is heavily supported by many fans due to its factors (2, 3, 4, and 6) make the base highly divisible, with cleaner divisions (e.g. 1/3 is 0.4, and 3/4 is 0.9).

People have even formed the Dozenal Society of America (DSA) and the Dozenal Society of Great Britain (DSGB) to help spread for the efficiency of such a base.

Multiplication Table

X 1 2 3 4 5 6 7 8 9 χ ε 10
1 1 2 3 4 5 6 7 8 9 χ ε 10
2 2 4 6 8 χ 10 12 14 16 18 1χ 20
3 3 6 9 10 13 16 19 20 23 26 29 30
4 4 8 10 14 18 20 24 28 30 34 38 40
5 5 χ 13 18 21 26 2ε 34 39 42 47 50
6 6 10 16 20 26 30 36 40 46 50 56 60
7 7 12 19 24 2ε 36 41 48 53 5χ 65 70
8 8 14 20 28 34 40 48 54 72 68 74 80
9 9 16 23 30 39 46 53 60 69 76 83 90
χ χ 18 26 34 42 50 5χ 68 76 84 92 χ0
ε ε 1χ 29 38 47 56 65 74 83 92 χ1 ε0
10 10 20 30 40 50 60 70 80 90 χ0 ε0 100

Counting Demonstration

Divisibility Rules

(Note: all numbers here are in base-10)

2- The last digit must be even.

3- The last digit must be divisible by 3.

4- The last digit must be divisible by 4.

5- Double the last digit, subtract it from the remaining digits as if they were a new number, and result must be divisible by 5.

6- The last digit must be divisible by 6.

7- Quadruple the last digit, add it to the remaining digits as if they were a new number, and result must be divisible by 7.

8- The last two digits as a whole must be divisible by 8.

9- The last two digits as a whole must be divisible by 9.

10- Must be divisible by 2 and 5.

11- The digits should add to a multiple of 11.

12- The last digit must be divisible by 12.

13- The alternate sum of the digits must be a multiple of 13.

Fractions

Recurring bits will be underlined.