We look at the division of 853171 by 45 
We want to divide 853171 by 45.

Step 1:
The number 45 fits into 8 0 times, leaving a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Take the next digit (5) from the dividend and append it to 8, then repeat: 85 / 45

Moving on to step 2:
85 divided by 45 is 1 with a remainder of 40.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 45 from 85 to get 40.
Take the next digit (3) from the dividend and append it to 40, then repeat: 403 / 45

Going ahead to step 3:
When dividing 403 by 45, we get 8 with a remainder of 43.
Record the quotient 8 as the next digit in the result. 
Result so far: 18.0
Deduct 360 from 403 and we're left with 43.
Append the next digit (1) from the dividend to 43 and continue with: 431 / 45

Advancing to step 4:
431 divided by 45 is 9 with a remainder of 26.
Record the quotient 9 as the next digit in the result. 
Result so far: 189.0
Subtract 405 from 431 to get 26.
Append the next digit (7) from the dividend to 26 and continue with: 267 / 45

Advancing to step 5:
When dividing 267 by 45, we get 5 with a remainder of 42.
The number 5 becomes the next digit in our result. 
Result so far: 1895.0
Subtract 225 from 267 to get 42.
Fetch the next digit (1) from the dividend, attach it to 42 and continue: 421 / 45

On to step 6:
When dividing 421 by 45, we get 9 with a remainder of 16.
Record the quotient 9 as the next digit in the result. 
Result so far: 18959.0
If we take 405 away from 421, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 7:
If we divide 160 by 45, we get 3 and a remainder of 25.
Use 3 as the next digit of our solution. 
Result so far: 18959.3
If we take 135 away from 160, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 8:
The number 45 fits into 250 5 times, leaving a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 18959.35
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 9:
If we divide 250 by 45, we get 5 and a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 18959.355
If we subtract 225 from 250, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 18959.355, and the remainder is 0.0025.