We look at the division of 557544 by 45 
Let's see how many times 45 fits into 557544.

Let's proceed to step 1:
When dividing 5 by 45, we get 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 45

Step 2:
55 divided by 45 is 1 with a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 45 from 55, we get 10.
Grab the next digit (7) from the dividend, add it to 10, then carry on: 107 / 45

On to step 3:
45 can be fit into 107 2 times, resulting in a remainder of 17.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
If we subtract 90 from 107, we get 17.
Fetch the next digit (5) from the dividend, attach it to 17 and continue: 175 / 45

Advancing to step 4:
If we divide 175 by 45, we get 3 and a remainder of 40.
Put 3 as the next digit of the answer. 
Result so far: 123.0
If we take 135 away from 175, we end up with 40.
Include the next digit (4) from the dividend after 40, then repeat: 404 / 45

Moving on to step 5:
404 divided by 45 is 8 with a remainder of 44.
The number 8 becomes the next digit in our result. 
Result so far: 1238.0
If we subtract 360 from 404, we get 44.
Fetch the next digit (4) from the dividend, attach it to 44 and continue: 444 / 45

On to step 6:
444 divided by 45 is 9 with a remainder of 39.
Put 9 as the next digit of the answer. 
Result so far: 12389.0
If we take 405 away from 444, we end up with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Advancing to step 7:
When dividing 390 by 45, we get 8 with a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 12389.8
The remainder is 30 after subtracting 360 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
300 divided by 45 is 6 with a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 12389.86
Subtracting 270 from 300 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 9:
300 divided by 45 is 6 with a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 12389.866
If we take 270 away from 300, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The final result is 12389.866 with a remainder of 0.003.