We look at the division of 15603 by 17 
We want to figure out the number of times 15603 can be divided by 17.

Advancing to step 1:
17 can be fit into 1 0 times, resulting in a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (5) from the dividend, add it to 1, then carry on: 15 / 17

Step 2:
17 can be fit into 15 0 times, resulting in a remainder of 15.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 15 leaves us with 15.
Include the next digit (6) from the dividend after 15, then repeat: 156 / 17

On to step 3:
If we divide 156 by 17, we get 9 and a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
Subtracting 153 from 156 leaves us with 3.
Fetch the next digit (0) from the dividend, attach it to 3 and continue: 30 / 17

Moving on to step 4:
When dividing 30 by 17, we get 1 with a remainder of 13.
Write down 1 as next digit of the result. 
Result so far: 91.0
The remainder is 13 after subtracting 17 from 30.
Bring next digit (3) of the dividend behind the 13 and repeat the process: 133 / 17

Step 5:
17 can be fit into 133 7 times, resulting in a remainder of 14.
Write down 7 as next digit of the result. 
Result so far: 917.0
Subtract 119 from 133 to get 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 6:
17 goes into 140 8 times with a remainder of 4.
Put 8 as the next digit of the answer. 
Result so far: 917.8
If we take 136 away from 140, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
17 can be fit into 40 2 times, resulting in a remainder of 6.
Record the quotient 2 as the next digit in the result. 
Result so far: 917.82
Subtract 34 from 40 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 8:
17 goes into 60 3 times with a remainder of 9.
Write down 3 as next digit of the result. 
Result so far: 917.823
Subtracting 51 from 60 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 9:
17 goes into 90 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 917.8235
Deduct 85 from 90 and we're left 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.

Advancing to step 10:
17 goes into 50 2 times with a remainder of 16.
Put 2 as the next digit of the answer. 
Result so far: 917.82352
Subtract 34 from 50 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 11:
17 goes into 160 9 times with a remainder of 7.
Record the quotient 9 as the next digit in the result. 
Result so far: 917.823529
Subtracting 153 from 160 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 12:
The number 17 fits into 70 4 times, leaving a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 917.8235294
If we take 68 away from 70, 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.

Let's proceed to step 13:
The number 17 fits into 20 1 times, leaving a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 917.82352941
The remainder is 3 after subtracting 17 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The quotient of the division is 917.82352941, and the remainder is 3e-09.