681742 ÷ 19 
We want to figure out the number of times 681742 can be divided by 19.

Advancing to step 1:
19 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 19

On to step 2:
The number 19 fits into 68 3 times, leaving a remainder of 11.
The next digit of our result is 3. 
Result so far: 3.0
Subtract 57 from 68 to get 11.
Fetch the next digit (1) from the dividend, attach it to 11 and continue: 111 / 19

Going ahead to step 3:
111 divided by 19 is 5 with a remainder of 16.
Use 5 as the next digit of our solution. 
Result so far: 35.0
The remainder is 16 after subtracting 95 from 111.
Append the next digit (7) from the dividend to 16 and continue with: 167 / 19

Advancing to step 4:
If we divide 167 by 19, we get 8 and a remainder of 15.
The number 8 becomes the next digit in our result. 
Result so far: 358.0
If we take 152 away from 167, we end up with 15.
Append the next digit (4) from the dividend to 15 and continue with: 154 / 19

Advancing to step 5:
If we divide 154 by 19, we get 8 and a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 3588.0
If we subtract 152 from 154, we get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 19

On to step 6:
If we divide 22 by 19, we get 1 and a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 35881.0
Subtracting 19 from 22 leaves us 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 7:
19 goes into 30 1 times with a remainder of 11.
Put 1 as the next digit of the answer. 
Result so far: 35881.1
Subtracting 19 from 30 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.

Step 8:
The number 19 fits into 110 5 times, leaving a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 35881.15
Deduct 95 from 110 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 9:
150 divided by 19 is 7 with a remainder of 17.
Write down 7 as next digit of the result. 
Result so far: 35881.157
Subtracting 133 from 150 leaves us with 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 10:
170 divided by 19 is 8 with a remainder of 18.
The next digit of our result is 8. 
Result so far: 35881.1578
If we take 152 away from 170, we end up with 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 11:
19 goes into 180 9 times with a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 35881.15789
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.

On to step 12:
The number 19 fits into 90 4 times, leaving a remainder of 14.
Write down 4 as next digit of the result. 
Result so far: 35881.157894
Subtracting 76 from 90 leaves us 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 13:
19 can be fit into 140 7 times, resulting in a remainder of 7.
Write down 7 as next digit of the result. 
Result so far: 35881.1578947
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.

Moving on to step 14:
70 divided by 19 is 3 with a remainder of 13.
The number 3 becomes the next digit in our result. 
Result so far: 35881.15789473
Subtracting 57 from 70 leaves us 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.

Our division results in 35881.15789473 with a remaining 1.3e-08.