819397 ÷ 6 
Our goal is to divide 819397 by 6.

Going ahead to step 1:
If we divide 8 by 6, we get 1 and a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 6 away from 8, we end up with 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 6

On to step 2:
6 can be fit into 21 3 times, resulting in a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
Deduct 18 from 21 and we're left with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 6

On to step 3:
When dividing 39 by 6, we get 6 with a remainder of 3.
The next digit of our result is 6. 
Result so far: 136.0
Subtracting 36 from 39 leaves us with 3.
Take the next digit (3) from the dividend and append it to 3, then repeat: 33 / 6

Advancing to step 4:
If we divide 33 by 6, we get 5 and a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 1365.0
Deduct 30 from 33 and we're left with 3.
Grab the next digit (9) from the dividend, add it to 3, then carry on: 39 / 6

Let's proceed to step 5:
If we divide 39 by 6, we get 6 and a remainder of 3.
The number 6 becomes the next digit in our result. 
Result so far: 13656.0
Subtracting 36 from 39 leaves us with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 6

Let's proceed to step 6:
6 can be fit into 37 6 times, resulting in a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 136566.0
Subtract 36 from 37 to get 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 7:
If we divide 10 by 6, we get 1 and a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 136566.1
The remainder is 4 after subtracting 6 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
The number 6 fits into 40 6 times, leaving a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 136566.16
Subtracting 36 from 40 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
When dividing 40 by 6, we get 6 with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 136566.166
Subtracting 36 from 40 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

In conclusion, the division gives 136566.166 with a balance of 0.0004.