687775 ÷ 6 
Our goal is to divide 687775 by 6.

Let's proceed to step 1:
6 can be fit into 6 1 times, resulting in a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 6 away from 6, we end up with 0.
Append the next digit (8) from the dividend to 0 and continue with: 8 / 6

Step 2:
6 can be fit into 8 1 times, resulting in a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 11.0
The remainder is 2 after subtracting 6 from 8.
Grab the next digit (7) from the dividend, add it to 2, then carry on: 27 / 6

Advancing to step 3:
6 can be fit into 27 4 times, resulting in a remainder of 3.
Use 4 as the next digit of our solution. 
Result so far: 114.0
If we take 24 away from 27, we end up with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 6

Going ahead to step 4:
37 divided by 6 is 6 with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 1146.0
Deduct 36 from 37 and we're left with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 6

On to step 5:
If we divide 17 by 6, we get 2 and a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 11462.0
The remainder is 5 after subtracting 12 from 17.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 6

Step 6:
6 can be fit into 55 9 times, resulting in a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 114629.0
The remainder is 1 after subtracting 54 from 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
The number 6 fits into 10 1 times, leaving a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 114629.1
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.

Let's proceed to step 8:
6 can be fit into 40 6 times, resulting in a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 114629.16
The remainder is 4 after subtracting 36 from 40.
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:
40 divided by 6 is 6 with a remainder of 4.
The next digit of our result is 6. 
Result so far: 114629.166
If we subtract 36 from 40, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final result is 114629.166 with a remainder of 0.0004.