85576 ÷ 45 
Our goal is to divide 85576 by 45.

Advancing to step 1:
45 can be fit into 8 0 times, resulting in a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Grab the next digit (5) from the dividend, add it to 8, then carry on: 85 / 45

Let's proceed to step 2:
85 divided by 45 is 1 with a remainder of 40.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 45 from 85 leaves us with 40.
Append the next digit (5) from the dividend to 40 and continue with: 405 / 45

On to step 3:
45 can be fit into 405 9 times, resulting in a remainder of 0.
The number 9 becomes the next digit in our result. 
Result so far: 19.0
Subtracting 405 from 405 leaves us with 0.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 45

Moving on to step 4:
7 divided by 45 is 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 190.0
If we take 0 away from 7, we end up with 7.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 45

Moving on to step 5:
45 goes into 76 1 times with a remainder of 31.
Record the quotient 1 as the next digit in the result. 
Result so far: 1901.0
Subtracting 45 from 76 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Let's proceed to step 6:
45 can be fit into 310 6 times, resulting in a remainder of 40.
The next digit of our result is 6. 
Result so far: 1901.6
If we subtract 270 from 310, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 7:
If we divide 400 by 45, we get 8 and a remainder of 40.
Use 8 as the next digit of our solution. 
Result so far: 1901.68
If we subtract 360 from 400, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 8:
45 can be fit into 400 8 times, resulting in a remainder of 40.
Use 8 as the next digit of our solution. 
Result so far: 1901.688
If we subtract 360 from 400, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

After the division, we end up with 1901.688 and a remainder of 0.004.