We look at the division of 34565 by 82 
Our goal is to divide 34565 by 82.

Let's proceed to step 1:
The number 82 fits into 3 0 times, leaving a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 82

Moving on to step 2:
The number 82 fits into 34 0 times, leaving a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 34 leaves us with 34.
Fetch the next digit (5) from the dividend, attach it to 34 and continue: 345 / 82

Step 3:
The number 82 fits into 345 4 times, leaving a remainder of 17.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we take 328 away from 345, we end up with 17.
Bring next digit (6) of the dividend behind the 17 and repeat the process: 176 / 82

Moving on to step 4:
The number 82 fits into 176 2 times, leaving a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 42.0
Subtracting 164 from 176 leaves us with 12.
Append the next digit (5) from the dividend to 12 and continue with: 125 / 82

On to step 5:
82 can be fit into 125 1 times, resulting in a remainder of 43.
The next digit of our result is 1. 
Result so far: 421.0
Deduct 82 from 125 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

On to step 6:
430 divided by 82 is 5 with a remainder of 20.
The number 5 becomes the next digit in our result. 
Result so far: 421.5
If we take 410 away from 430, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 7:
82 can be fit into 200 2 times, resulting in a remainder of 36.
The number 2 becomes the next digit in our result. 
Result so far: 421.52
Deduct 164 from 200 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 8:
When dividing 360 by 82, we get 4 with a remainder of 32.
The next digit of our result is 4. 
Result so far: 421.524
Deduct 328 from 360 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 9:
320 divided by 82 is 3 with a remainder of 74.
Use 3 as the next digit of our solution. 
Result so far: 421.5243
If we subtract 246 from 320, we get 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Let's proceed to step 10:
When dividing 740 by 82, we get 9 with a remainder of 2.
Write down 9 as next digit of the result. 
Result so far: 421.52439
If we take 738 away from 740, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 11:
When dividing 20 by 82, we get 0 with a remainder of 20.
Write down 0 as next digit of the result. 
Result so far: 421.52439
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 12:
When dividing 200 by 82, we get 2 with a remainder of 36.
Use 2 as the next digit of our solution. 
Result so far: 421.5243902
The remainder is 36 after subtracting 164 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 13:
360 divided by 82 is 4 with a remainder of 32.
Use 4 as the next digit of our solution. 
Result so far: 421.52439024
If we subtract 328 from 360, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The final outcome is 421.52439024, with a leftover of 3.2e-08.