Let's divide 83629734 by 603
Our goal is to divide 83629734 by 603.

On to step 1:
The number 603 fits into 8 0 times, leaving a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Fetch the next digit (3) from the dividend, attach it to 8 and continue: 83 / 603

On to step 2:
If we divide 83 by 603, we get 0 and a remainder of 83.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 83 to get 83.
Take the next digit (6) from the dividend and append it to 83, then repeat: 836 / 603

Step 3:
The number 603 fits into 836 1 times, leaving a remainder of 233.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 233 after subtracting 603 from 836.
Take the next digit (2) from the dividend and append it to 233, then repeat: 2332 / 603

Step 4:
If we divide 2332 by 603, we get 3 and a remainder of 523.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we subtract 1809 from 2332, we get 523.
Grab the next digit (9) from the dividend, add it to 523, then carry on: 5239 / 603

Step 5:
When dividing 5239 by 603, we get 8 with a remainder of 415.
Put 8 as the next digit of the answer. 
Result so far: 138.0
If we subtract 4824 from 5239, we get 415.
Append the next digit (7) from the dividend to 415 and continue with: 4157 / 603

Let's proceed to step 6:
603 can be fit into 4157 6 times, resulting in a remainder of 539.
Use 6 as the next digit of our solution. 
Result so far: 1386.0
Deduct 3618 from 4157 and we're left with 539.
Include the next digit (3) from the dividend after 539, then repeat: 5393 / 603

On to step 7:
603 can be fit into 5393 8 times, resulting in a remainder of 569.
The next digit of our result is 8. 
Result so far: 13868.0
Deduct 4824 from 5393 and we're left with 569.
Append the next digit (4) from the dividend to 569 and continue with: 5694 / 603

Moving on to step 8:
603 goes into 5694 9 times with a remainder of 267.
Use 9 as the next digit of our solution. 
Result so far: 138689.0
If we subtract 5427 from 5694, we get 267.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2670, and continue the process.

Moving on to step 9:
603 goes into 2670 4 times with a remainder of 258.
Write down 4 as next digit of the result. 
Result so far: 138689.4
If we take 2412 away from 2670, we end up with 258.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2580, and continue the process.

On to step 10:
If we divide 2580 by 603, we get 4 and a remainder of 168.
Record the quotient 4 as the next digit in the result. 
Result so far: 138689.44
Deduct 2412 from 2580 and we're left with 168.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1680, and continue the process.

After the division, we end up with 138689.44 and a remainder of 0.168.