We look at the division of 83107 by 66 
We're looking to find how many times 66 goes into 83107.

Step 1:
The number 66 fits into 8 0 times, leaving a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Grab the next digit (3) from the dividend, add it to 8, then carry on: 83 / 66

Advancing to step 2:
If we divide 83 by 66, we get 1 and a remainder of 17.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 66 from 83 to get 17.
Take the next digit (1) from the dividend and append it to 17, then repeat: 171 / 66

On to step 3:
If we divide 171 by 66, we get 2 and a remainder of 39.
Write down 2 as next digit of the result. 
Result so far: 12.0
If we take 132 away from 171, we end up with 39.
Take the next digit (0) from the dividend and append it to 39, then repeat: 390 / 66

Going ahead to step 4:
66 goes into 390 5 times with a remainder of 60.
The next digit of our result is 5. 
Result so far: 125.0
If we take 330 away from 390, we end up with 60.
Bring next digit (7) of the dividend behind the 60 and repeat the process: 607 / 66

Moving on to step 5:
607 divided by 66 is 9 with a remainder of 13.
Write down 9 as next digit of the result. 
Result so far: 1259.0
Deduct 594 from 607 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 6:
If we divide 130 by 66, we get 1 and a remainder of 64.
The next digit of our result is 1. 
Result so far: 1259.1
If we subtract 66 from 130, we get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 7:
If we divide 640 by 66, we get 9 and a remainder of 46.
Record the quotient 9 as the next digit in the result. 
Result so far: 1259.19
Subtract 594 from 640 to get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 8:
460 divided by 66 is 6 with a remainder of 64.
The next digit of our result is 6. 
Result so far: 1259.196
The remainder is 64 after subtracting 396 from 460.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Advancing to step 9:
66 can be fit into 640 9 times, resulting in a remainder of 46.
Put 9 as the next digit of the answer. 
Result so far: 1259.1969
Subtract 594 from 640 to get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 10:
66 goes into 460 6 times with a remainder of 64.
The next digit of our result is 6. 
Result so far: 1259.19696
If we take 396 away from 460, we end up with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 11:
66 goes into 640 9 times with a remainder of 46.
Record the quotient 9 as the next digit in the result. 
Result so far: 1259.196969
Deduct 594 from 640 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 12:
When dividing 460 by 66, we get 6 with a remainder of 64.
Use 6 as the next digit of our solution. 
Result so far: 1259.1969696
If we subtract 396 from 460, we get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 13:
When dividing 640 by 66, we get 9 with a remainder of 46.
Use 9 as the next digit of our solution. 
Result so far: 1259.19696969
If we take 594 away from 640, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

In conclusion, the division gives 1259.19696969 with a balance of 4.6e-08.