We're dividing 681875 by 19 
We're looking to find how many times 19 goes into 681875.

Going ahead to step 1:
6 divided by 19 is 0 with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 19

Advancing to step 2:
68 divided by 19 is 3 with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Subtracting 57 from 68 leaves us with 11.
Grab the next digit (1) from the dividend, add it to 11, then carry on: 111 / 19

Moving on to step 3:
19 can be fit into 111 5 times, resulting in a remainder of 16.
Record the quotient 5 as the next digit in the result. 
Result so far: 35.0
If we take 95 away from 111, we end up with 16.
Grab the next digit (8) from the dividend, add it to 16, then carry on: 168 / 19

Advancing to step 4:
When dividing 168 by 19, we get 8 with a remainder of 16.
The next digit of our result is 8. 
Result so far: 358.0
Deduct 152 from 168 and we're left with 16.
Take the next digit (7) from the dividend and append it to 16, then repeat: 167 / 19

Going ahead to step 5:
167 divided by 19 is 8 with a remainder of 15.
Write down 8 as next digit of the result. 
Result so far: 3588.0
Subtracting 152 from 167 leaves us with 15.
Append the next digit (5) from the dividend to 15 and continue with: 155 / 19

Moving on to step 6:
When dividing 155 by 19, we get 8 with a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 35888.0
If we subtract 152 from 155, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 7:
The number 19 fits into 30 1 times, leaving a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 35888.1
The remainder is 11 after subtracting 19 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 8:
If we divide 110 by 19, we get 5 and a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 35888.15
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.

Going ahead to step 9:
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: 35888.157
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.

On to step 10:
When dividing 170 by 19, we get 8 with a remainder of 18.
Record the quotient 8 as the next digit in the result. 
Result so far: 35888.1578
Subtracting 152 from 170 leaves us 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.

Going ahead to step 11:
When dividing 180 by 19, we get 9 with a remainder of 9.
The next digit of our result is 9. 
Result so far: 35888.15789
The remainder is 9 after subtracting 171 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 12:
90 divided by 19 is 4 with a remainder of 14.
Put 4 as the next digit of the answer. 
Result so far: 35888.157894
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.

Step 13:
When dividing 140 by 19, we get 7 with a remainder of 7.
The next digit of our result is 7. 
Result so far: 35888.1578947
Deduct 133 from 140 and we're left 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.

Going ahead to step 14:
If we divide 70 by 19, we get 3 and a remainder of 13.
Record the quotient 3 as the next digit in the result. 
Result so far: 35888.15789473
Deduct 57 from 70 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.

In conclusion, the division gives 35888.15789473 with a balance of 1.3e-08.