We look at the division of 554598 by 18 
We want to figure out the number of times 554598 can be divided by 18.

Advancing to step 1:
18 goes into 5 0 times with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 18

Advancing to step 2:
18 goes into 55 3 times with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Subtracting 54 from 55 leaves us with 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 18

On to step 3:
18 can be fit into 14 0 times, resulting in a remainder of 14.
The next digit of our result is 0. 
Result so far: 30.0
Subtracting 0 from 14 leaves us with 14.
Fetch the next digit (5) from the dividend, attach it to 14 and continue: 145 / 18

Going ahead to step 4:
When dividing 145 by 18, we get 8 with a remainder of 1.
Write down 8 as next digit of the result. 
Result so far: 308.0
If we subtract 144 from 145, we get 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 18

Let's proceed to step 5:
18 goes into 19 1 times with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 3081.0
If we subtract 18 from 19, we get 1.
Append the next digit (8) from the dividend to 1 and continue with: 18 / 18

Step 6:
18 can be fit into 18 1 times, resulting in a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 30811.0
Subtracting 18 from 18 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 7:
When dividing 0 by 18, we get 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 30811.0
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
The number 18 fits into 0 0 times, leaving a remainder of 0.
The next digit of our result is 0. 
Result so far: 30811.0
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 30811.0, and the remainder is 0.0.