Posted: Mar 23, 2012 5:31 pm
namirha wrote:
[...snip...]
1_ x 12 = 12______________1 + 2 = 3
2_ x 12 = 24______________2 + 4 = 6
3_ x 12 = 36______________3 + 6 = 9
4_ x 12 = 48_____4 + 8 = 12 = 1+2 = 3
5_ x 12 = 60_______________6+0 = 6
6_ x 12 = 72_______________7+2 = 9
7_ x 12 = 84______8+4 = 12 = 1+2 = 3
8_ x 12 = 96______9+6 = 15 = 1+5 = 6
9_ x 12 = 108____________1+0+8 = 9
10 x 12 = 120____________1+2+0 = 3
11 x 12 = 132____________1+3+2 = 6
12 x 12 = 144____________1+4+4 = 9
[...snip...]
What's with the math? there is nothing out of the ordinary or special with this.
It's the result of one of the many intricacies of math, this one in particular enables you to know if a certain number is divisible by 3 --> you add up the individual digits of the number like you did your original post the example.
Now if the result is divisible by 3 then you know the original number is also divisible by 3.
Since you multiply by 12 each time, and 12 is divisible by 3, the result will also be divisible by 3.
For example if I take some random number 75584584124151245811
and add every individual digit 7+5+5+8+4+5+8+4+1+2+4+1+5+1+2+4+5+8+1+1 = 81 (which is divisible by 3)
now if we divide 75584584124151245811 by 3 we get the nice round number of 25194861374717081937
The fact that you each time get the same series 3 - 6 - 9 is due to even simpler mathematics.
mystery solved, you're welcome.
edited to add:
other shortcuts for divisibility exist also: http://www.mathgoodies.com/lessons/vol3 ... ility.html