We look at the division of 603663 by 17 
We're looking to find how many times 17 goes into 603663.

Step 1:
If we divide 6 by 17, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (0) from the dividend and append it to 6, then repeat: 60 / 17

Step 2:
17 can be fit into 60 3 times, resulting in a remainder of 9.
Write down 3 as next digit of the result. 
Result so far: 3.0
The remainder is 9 after subtracting 51 from 60.
Take the next digit (3) from the dividend and append it to 9, then repeat: 93 / 17

Step 3:
93 divided by 17 is 5 with a remainder of 8.
The number 5 becomes the next digit in our result. 
Result so far: 35.0
Subtracting 85 from 93 leaves us with 8.
Append the next digit (6) from the dividend to 8 and continue with: 86 / 17

Let's proceed to step 4:
17 goes into 86 5 times with a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 355.0
The remainder is 1 after subtracting 85 from 86.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 17

Moving on to step 5:
17 goes into 16 0 times with a remainder of 16.
Write down 0 as next digit of the result. 
Result so far: 3550.0
If we take 0 away from 16, we end up with 16.
Fetch the next digit (3) from the dividend, attach it to 16 and continue: 163 / 17

Step 6:
When dividing 163 by 17, we get 9 with a remainder of 10.
Write down 9 as next digit of the result. 
Result so far: 35509.0
If we subtract 153 from 163, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 7:
When dividing 100 by 17, we get 5 with a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 35509.5
If we subtract 85 from 100, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 8:
If we divide 150 by 17, we get 8 and a remainder of 14.
Put 8 as the next digit of the answer. 
Result so far: 35509.58
Subtracting 136 from 150 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 9:
17 goes into 140 8 times with a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 35509.588
Subtract 136 from 140 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Our division results in 35509.588 with a remaining 0.0004.