677803 ÷ 19 
Our goal is to divide 677803 by 19.

Advancing to step 1:
19 can be fit into 6 0 times, resulting in a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Grab the next digit (7) from the dividend, add it to 6, then carry on: 67 / 19

Advancing to step 2:
67 divided by 19 is 3 with a remainder of 10.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 10 after subtracting 57 from 67.
Fetch the next digit (7) from the dividend, attach it to 10 and continue: 107 / 19

Moving on to step 3:
If we divide 107 by 19, we get 5 and a remainder of 12.
Use 5 as the next digit of our solution. 
Result so far: 35.0
Deduct 95 from 107 and we're left with 12.
Fetch the next digit (8) from the dividend, attach it to 12 and continue: 128 / 19

Moving on to step 4:
19 can be fit into 128 6 times, resulting in a remainder of 14.
The next digit of our result is 6. 
Result so far: 356.0
Subtract 114 from 128 to get 14.
Take the next digit (0) from the dividend and append it to 14, then repeat: 140 / 19

Let's proceed to step 5:
When dividing 140 by 19, we get 7 with a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 3567.0
Deduct 133 from 140 and we're left with 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 19

On to step 6:
The number 19 fits into 73 3 times, leaving a remainder of 16.
Record the quotient 3 as the next digit in the result. 
Result so far: 35673.0
Subtract 57 from 73 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 7:
The number 19 fits into 160 8 times, leaving a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 35673.8
The remainder is 8 after subtracting 152 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 8:
19 goes into 80 4 times with a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 35673.84
The remainder is 4 after subtracting 76 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 9:
The number 19 fits into 40 2 times, leaving a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 35673.842
Deduct 38 from 40 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 10:
If we divide 20 by 19, we get 1 and a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 35673.8421
Subtracting 19 from 20 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 11:
19 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 35673.8421
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 12:
When dividing 100 by 19, we get 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 35673.842105
Subtract 95 from 100 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 13:
If we divide 50 by 19, we get 2 and a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 35673.8421052
The remainder is 12 after subtracting 38 from 50.
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 14:
If we divide 120 by 19, we get 6 and a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 35673.84210526
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.

After the division, we end up with 35673.84210526 and a remainder of 6e-09.