We're dividing 629603 by 6 
Let's see how many times 6 fits into 629603.

Going ahead to step 1:
6 can be fit into 6 1 times, resulting in a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
If we take 6 away from 6, we end up with 0.
Include the next digit (2) from the dividend after 0, then repeat: 2 / 6

Moving on to step 2:
If we divide 2 by 6, we get 0 and a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Subtract 0 from 2 to get 2.
Grab the next digit (9) from the dividend, add it to 2, then carry on: 29 / 6

Step 3:
The number 6 fits into 29 4 times, leaving a remainder of 5.
Use 4 as the next digit of our solution. 
Result so far: 104.0
Deduct 24 from 29 and we're left with 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Moving on to step 4:
6 goes into 56 9 times with a remainder of 2.
Put 9 as the next digit of the answer. 
Result so far: 1049.0
The remainder is 2 after subtracting 54 from 56.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 6

Advancing to step 5:
6 goes into 20 3 times with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 10493.0
Deduct 18 from 20 and we're left with 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 6

Advancing to step 6:
6 goes into 23 3 times with a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 104933.0
Subtracting 18 from 23 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 7:
If we divide 50 by 6, we get 8 and a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 104933.8
Subtract 48 from 50 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.

Advancing to step 8:
6 can be fit into 20 3 times, resulting in a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 104933.83
If we subtract 18 from 20, we 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.

Step 9:
When dividing 20 by 6, we get 3 with a remainder of 2.
The next digit of our result is 3. 
Result so far: 104933.833
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.

The final result is 104933.833 with a remainder of 0.0002.