We look at the division of 174538 by 45 
Let's see how many times 45 fits into 174538.

On to step 1:
45 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 45

On to step 2:
If we divide 17 by 45, we get 0 and a remainder of 17.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 17 after subtracting 0 from 17.
Fetch the next digit (4) from the dividend, attach it to 17 and continue: 174 / 45

On to step 3:
45 goes into 174 3 times with a remainder of 39.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we subtract 135 from 174, we get 39.
Fetch the next digit (5) from the dividend, attach it to 39 and continue: 395 / 45

Going ahead to step 4:
45 goes into 395 8 times with a remainder of 35.
Use 8 as the next digit of our solution. 
Result so far: 38.0
If we subtract 360 from 395, we get 35.
Include the next digit (3) from the dividend after 35, then repeat: 353 / 45

Going ahead to step 5:
If we divide 353 by 45, we get 7 and a remainder of 38.
The number 7 becomes the next digit in our result. 
Result so far: 387.0
Subtract 315 from 353 to get 38.
Take the next digit (8) from the dividend and append it to 38, then repeat: 388 / 45

Advancing to step 6:
388 divided by 45 is 8 with a remainder of 28.
The next digit of our result is 8. 
Result so far: 3878.0
The remainder is 28 after subtracting 360 from 388.
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 7:
45 goes into 280 6 times with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 3878.6
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.

Moving on to step 8:
The number 45 fits into 100 2 times, leaving a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 3878.62
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 9:
The number 45 fits into 100 2 times, leaving a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 3878.622
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.

The quotient of the division is 3878.622, and the remainder is 0.001.