We look at the division of 34311 by 45 
We're looking to find how many times 45 goes into 34311.

On to step 1:
45 goes into 3 0 times with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 45

Moving on to step 2:
When dividing 34 by 45, we get 0 with a remainder of 34.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 34 to get 34.
Take the next digit (3) from the dividend and append it to 34, then repeat: 343 / 45

On to step 3:
45 can be fit into 343 7 times, resulting in a remainder of 28.
The next digit of our result is 7. 
Result so far: 7.0
Subtract 315 from 343 to get 28.
Include the next digit (1) from the dividend after 28, then repeat: 281 / 45

Going ahead to step 4:
If we divide 281 by 45, we get 6 and a remainder of 11.
The number 6 becomes the next digit in our result. 
Result so far: 76.0
Deduct 270 from 281 and we're left with 11.
Grab the next digit (1) from the dividend, add it to 11, then carry on: 111 / 45

Let's proceed to step 5:
111 divided by 45 is 2 with a remainder of 21.
The number 2 becomes the next digit in our result. 
Result so far: 762.0
The remainder is 21 after subtracting 90 from 111.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 6:
When dividing 210 by 45, we get 4 with a remainder of 30.
Write down 4 as next digit of the result. 
Result so far: 762.4
The remainder is 30 after subtracting 180 from 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 7:
The number 45 fits into 300 6 times, leaving a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 762.46
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
When dividing 300 by 45, we get 6 with a remainder of 30.
Use 6 as the next digit of our solution. 
Result so far: 762.466
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

After the division, we end up with 762.466 and a remainder of 0.003.