688441 ÷ 8 
Our goal is to divide 688441 by 8.

Going ahead to step 1:
When dividing 6 by 8, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 8

Let's proceed to step 2:
When dividing 68 by 8, we get 8 with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Deduct 64 from 68 and we're left with 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 8

Moving on to step 3:
If we divide 48 by 8, we get 6 and a remainder of 0.
The next digit of our result is 6. 
Result so far: 86.0
Subtracting 48 from 48 leaves us with 0.
Grab the next digit (4) from the dividend, add it to 0, then carry on: 4 / 8

Advancing to step 4:
8 can be fit into 4 0 times, resulting in a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 860.0
Subtract 0 from 4 to get 4.
Include the next digit (4) from the dividend after 4, then repeat: 44 / 8

Advancing to step 5:
If we divide 44 by 8, we get 5 and a remainder of 4.
Write down 5 as next digit of the result. 
Result so far: 8605.0
Deduct 40 from 44 and we're left with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 8

Going ahead to step 6:
The number 8 fits into 41 5 times, leaving a remainder of 1.
The next digit of our result is 5. 
Result so far: 86055.0
Subtracting 40 from 41 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.

Moving on to step 7:
When dividing 10 by 8, we get 1 with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 86055.1
Deduct 8 from 10 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.

Moving on to step 8:
8 goes into 20 2 times with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 86055.12
Deduct 16 from 20 and we're left 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.

On to step 9:
The number 8 fits into 40 5 times, leaving a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 86055.125
Subtract 40 from 40 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 10:
When dividing 0 by 8, we get 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 86055.125
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 11:
8 can be fit into 0 0 times, resulting in a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 86055.125
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Our division results in 86055.125 with a remaining 0.0.