553564 ÷ 45 
Our goal is to divide 553564 by 45.

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
Subtracting 0 from 5 leaves us with 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 45

On to step 2:
55 divided by 45 is 1 with a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 45 from 55 leaves us with 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 45

Moving on to step 3:
The number 45 fits into 103 2 times, leaving a remainder of 13.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Subtract 90 from 103 to get 13.
Include the next digit (5) from the dividend after 13, then repeat: 135 / 45

On to step 4:
135 divided by 45 is 3 with a remainder of 0.
The next digit of our result is 3. 
Result so far: 123.0
If we subtract 135 from 135, we get 0.
Include the next digit (6) from the dividend after 0, then repeat: 6 / 45

On to step 5:
If we divide 6 by 45, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 1230.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 45

Advancing to step 6:
The number 45 fits into 64 1 times, leaving a remainder of 19.
The number 1 becomes the next digit in our result. 
Result so far: 12301.0
Deduct 45 from 64 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

On to step 7:
The number 45 fits into 190 4 times, leaving a remainder of 10.
Write down 4 as next digit of the result. 
Result so far: 12301.4
Deduct 180 from 190 and we're left 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.

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: 12301.42
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.

Let's proceed to step 9:
45 can be fit into 100 2 times, resulting in a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 12301.422
Subtract 90 from 100 to get 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 final outcome is 12301.422, with a leftover of 0.001.