628679 ÷ 3 
Our goal is to divide 628679 by 3.

Going ahead to step 1:
If we divide 6 by 3, we get 2 and a remainder of 0.
The next digit of our result is 2. 
Result so far: 2.0
If we take 6 away from 6, we end up with 0.
Append the next digit (2) from the dividend to 0 and continue with: 2 / 3

Step 2:
3 can be fit into 2 0 times, resulting in a remainder of 2.
The next digit of our result is 0. 
Result so far: 20.0
Subtracting 0 from 2 leaves us with 2.
Fetch the next digit (8) from the dividend, attach it to 2 and continue: 28 / 3

On to step 3:
28 divided by 3 is 9 with a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 209.0
Subtracting 27 from 28 leaves us with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 3

On to step 4:
When dividing 16 by 3, we get 5 with a remainder of 1.
Record the quotient 5 as the next digit in the result. 
Result so far: 2095.0
The remainder is 1 after subtracting 15 from 16.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 3

Going ahead to step 5:
When dividing 17 by 3, we get 5 with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 20955.0
Deduct 15 from 17 and we're left with 2.
Fetch the next digit (9) from the dividend, attach it to 2 and continue: 29 / 3

On to step 6:
When dividing 29 by 3, we get 9 with a remainder of 2.
The next digit of our result is 9. 
Result so far: 209559.0
If we take 27 away from 29, 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.

Going ahead to step 7:
3 goes into 20 6 times with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 209559.6
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 8:
3 can be fit into 20 6 times, resulting in a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 209559.66
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.

In conclusion, the division gives 209559.66 with a balance of 0.002.