Dividing numbers with dots?! OK. This intrigues me. I recently came across this video. Which presumably tells you how to divide 133,342 with 121 only using hand drawn dots! Fair enough but I don't think this works for every number.
I think this method of dividing is made by the uploader himself Presh Talwalkar.
Here's a summary of the method:

Starting with the digit 1 we draw 1 dot, for the digit 3 we draw 3 dots
  and so on we draw dots corresponding to each digit of the number we
  want to divide by.
Once we draw all the dots we are ready to connect all the dots. The
  number we are dividing by is 121, so that means we want to connect one
  dot to two dots to one more dot. We continue doing this for the
  remaining dots connecting one dot to two dots to one more dot until
  all the dots are filled in.
To get to the answer we start by looking at the number of completed
  figures. So starting with the column on the far left there's one
  completed figure that starts in this column so we write a 1. Moving
  one column over, the first two dots correspond to a figure that has
  already started. It's only the third dot that counts for a new figure,
  so we write an another 1. Going to the third column all of the dots
  that correspond to the figures have already started, so we write a
  0.And finally in the fourth column we have 2 figures that are starting, so we write a 2. What we get is 1,102 as a result, and you
  can check, It's the correct answer.


What happens when you try to divide with this method a number like this:

How can you connect the dots? Are these dots arranged alright? What do you put If the digit is 0?
I still can't figure out how to divide my own numbers with his method. 
Is this just a coincidental trick or a real deal? 
Many questions are left unanswered by the author..
 A: I can't view the video but is this the dots and boxes method?
It gets unwieldy with large digits in the divisor.
You need to pair off groups of $6$ dots with groups of $6$ dots in the column to the right.  You can "unexplode" remainders going to the right (which kinda looks like exploding to me, but oh well).
Here's how it plays out (I'm forgetting about the zero).  The columns show the number of dots in that column:
1000      100       10        1
---------------------------------
  2         3        7        6
           23        7        6       unexploded two 1000s to twenty 100s
           17        1        6       paired off a 6-6; quotient is "1?"
           16       11        6       unexploded a 100
           10        5        6       paired off another 6-6; quotient is "2?"
            9       15        6       unexploded another 100
            3        9        6       paired off another 6-6; quotient is "3?"
                    39        6       unexploded the rest because we're less than 6 in 100s
                    33        0       paired off a 6-6; quotient now is "31"
                    30       30       unexploded three more (for brevity)
                     0        0       paired off five more 6-6; quotient is "36"
                                      And ... we're done!

I guess the extra zeroes at the end just get tacked on because there are no dots anywhere to pair off anymore.                
A: Here's a link where they "carry" when there are not enough dots in a column for a given digit. (link here) (screen capture of article here)
So when attempting to take the first 6, there are only 2 dots in the first row, which is insufficient. Convert them to 20 dots in the second row, and try again.
As was mentioned previously, this is really the same as standard division. 6 doesn't go into 2, so we look at 23. It's kind of convoluted and more complex for the problem you gave. With small digits in the divisor, it's a nice method. I see the same issue with the crossing lines method.
A: enter image description here
I'm researching different division strategies and came across this thread.
Yes, the dot method works. I'm pretty sure that the Youtuber did not create this method. I agree with previous comments to external sites--hopefully those helped!
It gets more clustered-looking the more dots you have and the more you have to borrow from previous columns, but it is very doable.
If there is a 0 for the divisor, that column of dots would be skipped.
If you run out of dots, you have to borrow dots (1 dot = 10 new dots) from the previous column.
Hopefully the image loads/works, but I did your problem using the dot method.
23,760 ÷ 66 = 36
-1st column dots get "borrowed" by 2nd column
-2nd column ends up with 23 dots

can take 3 groups (of 6 to 6 dots) out (3 x 6 = 18)
-3rd column ends up taking 5 dots from the 2nd column (so 3rd column ends up with 57 dots)
-4th column does not have enough dots and takes 3 dots from 3rd column (so the 4th column ends up with 36)
can take 6 groups out (of 6 to 6 dots) out (6 x 6 = 36)
Answer: 36 is quotient

