We divide 21538 by 45
We want to figure out the number of times 21538 can be divided by 45.

Step 1:
If we divide 2 by 45, we get 0 and a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 45

On to step 2:
45 goes into 21 0 times with a remainder of 21.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 21, we get 21.
Take the next digit (5) from the dividend and append it to 21, then repeat: 215 / 45

Moving on to step 3:
45 can be fit into 215 4 times, resulting in a remainder of 35.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
Subtract 180 from 215 to get 35.
Include the next digit (3) from the dividend after 35, then repeat: 353 / 45

Step 4:
The number 45 fits into 353 7 times, leaving a remainder of 38.
The number 7 becomes the next digit in our result. 
Result so far: 47.0
If we take 315 away from 353, we end up with 38.
Include the next digit (8) from the dividend after 38, then repeat: 388 / 45

Let's proceed to step 5:
45 can be fit into 388 8 times, resulting in a remainder of 28.
Write down 8 as next digit of the result. 
Result so far: 478.0
If we take 360 away from 388, we end up 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.

Advancing to step 6:
The number 45 fits into 280 6 times, leaving a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 478.6
Subtracting 270 from 280 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.

Step 7:
45 can be fit into 100 2 times, resulting in a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 478.62
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.

Step 8:
45 goes into 100 2 times with a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 478.622
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.

Our division results in 478.622 with a remaining 0.001.