19567 ÷ 45 
We want to figure out the number of times 19567 can be divided by 45.

On to step 1:
The number 45 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (9) from the dividend to 1 and continue with: 19 / 45

On to step 2:
If we divide 19 by 45, we get 0 and a remainder of 19.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 19 to get 19.
Fetch the next digit (5) from the dividend, attach it to 19 and continue: 195 / 45

Advancing to step 3:
45 can be fit into 195 4 times, resulting in a remainder of 15.
The next digit of our result is 4. 
Result so far: 4.0
The remainder is 15 after subtracting 180 from 195.
Include the next digit (6) from the dividend after 15, then repeat: 156 / 45

On to step 4:
If we divide 156 by 45, we get 3 and a remainder of 21.
The number 3 becomes the next digit in our result. 
Result so far: 43.0
If we take 135 away from 156, we end up with 21.
Bring next digit (7) of the dividend behind the 21 and repeat the process: 217 / 45

Step 5:
If we divide 217 by 45, we get 4 and a remainder of 37.
Put 4 as the next digit of the answer. 
Result so far: 434.0
If we subtract 180 from 217, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Going ahead to step 6:
The number 45 fits into 370 8 times, leaving a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 434.8
If we subtract 360 from 370, we 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.

Moving on to step 7:
100 divided by 45 is 2 with a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 434.82
Deduct 90 from 100 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.

Let's proceed to step 8:
100 divided by 45 is 2 with a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 434.822
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 result is 434.822 with a remainder of 0.001.