We look at the division of 574566 by 45 
We want to figure out the number of times 574566 can be divided by 45.

Advancing to step 1:
When dividing 5 by 45, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (7) from the dividend, add it to 5, then carry on: 57 / 45

Step 2:
45 goes into 57 1 times with a remainder of 12.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 45 from 57, we get 12.
Take the next digit (4) from the dividend and append it to 12, then repeat: 124 / 45

Moving on to step 3:
45 goes into 124 2 times with a remainder of 34.
Write down 2 as next digit of the result. 
Result so far: 12.0
If we subtract 90 from 124, we get 34.
Take the next digit (5) from the dividend and append it to 34, then repeat: 345 / 45

Going ahead to step 4:
345 divided by 45 is 7 with a remainder of 30.
Put 7 as the next digit of the answer. 
Result so far: 127.0
Deduct 315 from 345 and we're left with 30.
Bring next digit (6) of the dividend behind the 30 and repeat the process: 306 / 45

Going ahead to step 5:
The number 45 fits into 306 6 times, leaving a remainder of 36.
The next digit of our result is 6. 
Result so far: 1276.0
The remainder is 36 after subtracting 270 from 306.
Fetch the next digit (6) from the dividend, attach it to 36 and continue: 366 / 45

Let's proceed to step 6:
45 can be fit into 366 8 times, resulting in a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 12768.0
Deduct 360 from 366 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 7:
If we divide 60 by 45, we get 1 and a remainder of 15.
The next digit of our result is 1. 
Result so far: 12768.1
The remainder is 15 after subtracting 45 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
45 can be fit into 150 3 times, resulting in a remainder of 15.
The number 3 becomes the next digit in our result. 
Result so far: 12768.13
Subtracting 135 from 150 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 9:
The number 45 fits into 150 3 times, leaving a remainder of 15.
Write down 3 as next digit of the result. 
Result so far: 12768.133
If we take 135 away from 150, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

In conclusion, the division gives 12768.133 with a balance of 0.0015.