678635 ÷ 6 
Our goal is to divide 678635 by 6.

Moving on to step 1:
6 can be fit into 6 1 times, resulting in a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 6 from 6 to get 0.
Include the next digit (7) from the dividend after 0, then repeat: 7 / 6

Step 2:
7 divided by 6 is 1 with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 11.0
If we subtract 6 from 7, we get 1.
Take the next digit (8) from the dividend and append it to 1, then repeat: 18 / 6

Going ahead to step 3:
If we divide 18 by 6, we get 3 and a remainder of 0.
Record the quotient 3 as the next digit in the result. 
Result so far: 113.0
Deduct 18 from 18 and we're left with 0.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 6

On to step 4:
When dividing 6 by 6, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1131.0
Subtracting 6 from 6 leaves us with 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 6

On to step 5:
If we divide 3 by 6, we get 0 and a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 11310.0
If we subtract 0 from 3, we get 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 6

Moving on to step 6:
6 can be fit into 35 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 113105.0
Subtract 30 from 35 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.

On to step 7:
6 can be fit into 50 8 times, resulting in a remainder of 2.
The next digit of our result is 8. 
Result so far: 113105.8
The remainder is 2 after subtracting 48 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
6 can be fit into 20 3 times, resulting in a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 113105.83
If we take 18 away from 20, we end up 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 9:
6 goes into 20 3 times with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 113105.833
Deduct 18 from 20 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.

The final result is 113105.833 with a remainder of 0.0002.