10766 ÷ 19 
Our goal is to divide 10766 by 19.

Advancing to step 1:
19 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 19

Advancing to step 2:
19 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Take the next digit (7) from the dividend and append it to 10, then repeat: 107 / 19

Step 3:
When dividing 107 by 19, we get 5 with a remainder of 12.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 95 from 107 leaves us with 12.
Grab the next digit (6) from the dividend, add it to 12, then carry on: 126 / 19

Going ahead to step 4:
19 can be fit into 126 6 times, resulting in a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 56.0
If we subtract 114 from 126, we get 12.
Fetch the next digit (6) from the dividend, attach it to 12 and continue: 126 / 19

Going ahead to step 5:
If we divide 126 by 19, we get 6 and a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 566.0
Subtract 114 from 126 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 6:
If we divide 120 by 19, we get 6 and a remainder of 6.
The next digit of our result is 6. 
Result so far: 566.6
Subtracting 114 from 120 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 7:
When dividing 60 by 19, we get 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 566.63
If we take 57 away from 60, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 8:
If we divide 30 by 19, we get 1 and a remainder of 11.
Record the quotient 1 as the next digit in the result. 
Result so far: 566.631
Subtract 19 from 30 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 9:
19 can be fit into 110 5 times, resulting in a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 566.6315
Subtract 95 from 110 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 10:
19 can be fit into 150 7 times, resulting in a remainder of 17.
The number 7 becomes the next digit in our result. 
Result so far: 566.63157
If we subtract 133 from 150, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 11:
19 goes into 170 8 times with a remainder of 18.
Record the quotient 8 as the next digit in the result. 
Result so far: 566.631578
Subtract 152 from 170 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 12:
180 divided by 19 is 9 with a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 566.6315789
If we subtract 171 from 180, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 13:
The number 19 fits into 90 4 times, leaving a remainder of 14.
Put 4 as the next digit of the answer. 
Result so far: 566.63157894
If we take 76 away from 90, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

The final result is 566.63157894 with a remainder of 1.4e-08.