603163 ÷ 33 
Our goal is to divide 603163 by 33.

Advancing to step 1:
If we divide 6 by 33, we get 0 and a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 33

Moving on to step 2:
33 can be fit into 60 1 times, resulting in a remainder of 27.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 33 from 60 and we're left with 27.
Append the next digit (3) from the dividend to 27 and continue with: 273 / 33

Let's proceed to step 3:
273 divided by 33 is 8 with a remainder of 9.
The number 8 becomes the next digit in our result. 
Result so far: 18.0
If we subtract 264 from 273, we get 9.
Fetch the next digit (1) from the dividend, attach it to 9 and continue: 91 / 33

Step 4:
33 goes into 91 2 times with a remainder of 25.
The number 2 becomes the next digit in our result. 
Result so far: 182.0
The remainder is 25 after subtracting 66 from 91.
Take the next digit (6) from the dividend and append it to 25, then repeat: 256 / 33

Step 5:
If we divide 256 by 33, we get 7 and a remainder of 25.
Use 7 as the next digit of our solution. 
Result so far: 1827.0
If we subtract 231 from 256, we get 25.
Take the next digit (3) from the dividend and append it to 25, then repeat: 253 / 33

Going ahead to step 6:
33 goes into 253 7 times with a remainder of 22.
The number 7 becomes the next digit in our result. 
Result so far: 18277.0
If we take 231 away from 253, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 7:
The number 33 fits into 220 6 times, leaving a remainder of 22.
Record the quotient 6 as the next digit in the result. 
Result so far: 18277.6
If we subtract 198 from 220, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 8:
When dividing 220 by 33, we get 6 with a remainder of 22.
The next digit of our result is 6. 
Result so far: 18277.66
If we take 198 away from 220, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

In conclusion, the division gives 18277.66 with a balance of 0.022.