We're dividing 127102 by 19 
We're looking to find how many times 19 goes into 127102.

Advancing to step 1:
The number 19 fits into 1 0 times, leaving 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.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 19

Advancing to step 2:
12 divided by 19 is 0 with a remainder of 12.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 12 leaves us with 12.
Grab the next digit (7) from the dividend, add it to 12, then carry on: 127 / 19

Step 3:
127 divided by 19 is 6 with a remainder of 13.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 114 from 127 and we're left with 13.
Take the next digit (1) from the dividend and append it to 13, then repeat: 131 / 19

Moving on to step 4:
19 goes into 131 6 times with a remainder of 17.
Record the quotient 6 as the next digit in the result. 
Result so far: 66.0
If we subtract 114 from 131, we get 17.
Grab the next digit (0) from the dividend, add it to 17, then carry on: 170 / 19

Going ahead to step 5:
When dividing 170 by 19, we get 8 with a remainder of 18.
The next digit of our result is 8. 
Result so far: 668.0
If we take 152 away from 170, we end up with 18.
Grab the next digit (2) from the dividend, add it to 18, then carry on: 182 / 19

Step 6:
The number 19 fits into 182 9 times, leaving a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 6689.0
Subtracting 171 from 182 leaves us with 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 7:
19 can be fit into 110 5 times, resulting in a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 6689.5
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.

Moving on to step 8:
19 can be fit into 150 7 times, resulting in a remainder of 17.
Write down 7 as next digit of the result. 
Result so far: 6689.57
The remainder is 17 after subtracting 133 from 150.
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 9:
When dividing 170 by 19, we get 8 with a remainder of 18.
Use 8 as the next digit of our solution. 
Result so far: 6689.578
If we subtract 152 from 170, we 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.

Let's proceed to step 10:
180 divided by 19 is 9 with a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 6689.5789
Subtracting 171 from 180 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 11:
If we divide 90 by 19, we get 4 and a remainder of 14.
Use 4 as the next digit of our solution. 
Result so far: 6689.57894
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.

Moving on to step 12:
19 can be fit into 140 7 times, resulting in a remainder of 7.
Put 7 as the next digit of the answer. 
Result so far: 6689.578947
If we take 133 away from 140, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 13:
19 goes into 70 3 times with a remainder of 13.
The next digit of our result is 3. 
Result so far: 6689.5789473
Subtract 57 from 70 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 14:
If we divide 130 by 19, we get 6 and a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 6689.57894736
Deduct 114 from 130 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

After the division, we end up with 6689.57894736 and a remainder of 1.6e-08.