We're dividing 556599 by 45 
Our goal is to divide 556599 by 45.

Step 1:
45 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 45

Going ahead to step 2:
45 goes into 55 1 times with a remainder of 10.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 45 from 55, we get 10.
Take the next digit (6) from the dividend and append it to 10, then repeat: 106 / 45

Going ahead to step 3:
The number 45 fits into 106 2 times, leaving a remainder of 16.
The next digit of our result is 2. 
Result so far: 12.0
If we subtract 90 from 106, we get 16.
Append the next digit (5) from the dividend to 16 and continue with: 165 / 45

On to step 4:
45 goes into 165 3 times with a remainder of 30.
Put 3 as the next digit of the answer. 
Result so far: 123.0
The remainder is 30 after subtracting 135 from 165.
Fetch the next digit (9) from the dividend, attach it to 30 and continue: 309 / 45

Moving on to step 5:
If we divide 309 by 45, we get 6 and a remainder of 39.
Write down 6 as next digit of the result. 
Result so far: 1236.0
If we subtract 270 from 309, we get 39.
Fetch the next digit (9) from the dividend, attach it to 39 and continue: 399 / 45

Step 6:
45 can be fit into 399 8 times, resulting in a remainder of 39.
Record the quotient 8 as the next digit in the result. 
Result so far: 12368.0
Subtracting 360 from 399 leaves us 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:
390 divided by 45 is 8 with a remainder of 30.
Record the quotient 8 as the next digit in the result. 
Result so far: 12368.8
If we subtract 360 from 390, we get 30.
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.
Put 6 as the next digit of the answer. 
Result so far: 12368.86
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.

Going ahead to step 9:
When dividing 300 by 45, we get 6 with a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 12368.866
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 12368.866 with a remainder of 0.003.