556588 ÷ 45 
We want to figure out the number of times 556588 can be divided by 45.

Let's proceed to step 1:
The number 45 fits into 5 0 times, leaving 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.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 45

Moving on to step 2:
55 divided by 45 is 1 with a remainder of 10.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 10 after subtracting 45 from 55.
Bring next digit (6) of the dividend behind the 10 and repeat the process: 106 / 45

Step 3:
The number 45 fits into 106 2 times, leaving a remainder of 16.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
The remainder is 16 after subtracting 90 from 106.
Take the next digit (5) from the dividend and append it to 16, then repeat: 165 / 45

Let's proceed to step 4:
If we divide 165 by 45, we get 3 and a remainder of 30.
The next digit of our result is 3. 
Result so far: 123.0
Subtract 135 from 165 to get 30.
Take the next digit (8) from the dividend and append it to 30, then repeat: 308 / 45

On to step 5:
45 can be fit into 308 6 times, resulting in a remainder of 38.
The number 6 becomes the next digit in our result. 
Result so far: 1236.0
Subtracting 270 from 308 leaves us with 38.
Include the next digit (8) from the dividend after 38, then repeat: 388 / 45

Let's proceed to step 6:
If we divide 388 by 45, we get 8 and a remainder of 28.
The next digit of our result is 8. 
Result so far: 12368.0
Deduct 360 from 388 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 7:
45 can be fit into 280 6 times, resulting in a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 12368.6
The remainder is 10 after subtracting 270 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 8:
If we divide 100 by 45, we get 2 and a remainder of 10.
The next digit of our result is 2. 
Result so far: 12368.62
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
The number 45 fits into 100 2 times, leaving a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 12368.622
Subtracting 90 from 100 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 12368.622, and the remainder is 0.001.