10436 ÷ 82 
Our goal is to divide 10436 by 82.

Going ahead to step 1:
82 can be fit into 1 0 times, resulting in a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 82

Moving on to step 2:
10 divided by 82 is 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Fetch the next digit (4) from the dividend, attach it to 10 and continue: 104 / 82

Advancing to step 3:
When dividing 104 by 82, we get 1 with a remainder of 22.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 82 from 104 to get 22.
Take the next digit (3) from the dividend and append it to 22, then repeat: 223 / 82

Advancing to step 4:
When dividing 223 by 82, we get 2 with a remainder of 59.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Deduct 164 from 223 and we're left with 59.
Bring next digit (6) of the dividend behind the 59 and repeat the process: 596 / 82

Going ahead to step 5:
The number 82 fits into 596 7 times, leaving a remainder of 22.
Use 7 as the next digit of our solution. 
Result so far: 127.0
Subtracting 574 from 596 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 6:
82 can be fit into 220 2 times, resulting in a remainder of 56.
The next digit of our result is 2. 
Result so far: 127.2
Subtracting 164 from 220 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Let's proceed to step 7:
If we divide 560 by 82, we get 6 and a remainder of 68.
Put 6 as the next digit of the answer. 
Result so far: 127.26
The remainder is 68 after subtracting 492 from 560.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Let's proceed to step 8:
The number 82 fits into 680 8 times, leaving a remainder of 24.
The next digit of our result is 8. 
Result so far: 127.268
If we take 656 away from 680, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 9:
When dividing 240 by 82, we get 2 with a remainder of 76.
The next digit of our result is 2. 
Result so far: 127.2682
Subtract 164 from 240 to get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Let's proceed to step 10:
760 divided by 82 is 9 with a remainder of 22.
Put 9 as the next digit of the answer. 
Result so far: 127.26829
The remainder is 22 after subtracting 738 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 11:
220 divided by 82 is 2 with a remainder of 56.
Write down 2 as next digit of the result. 
Result so far: 127.268292
Subtracting 164 from 220 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Advancing to step 12:
82 can be fit into 560 6 times, resulting in a remainder of 68.
The number 6 becomes the next digit in our result. 
Result so far: 127.2682926
Subtracting 492 from 560 leaves us with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

On to step 13:
If we divide 680 by 82, we get 8 and a remainder of 24.
Use 8 as the next digit of our solution. 
Result so far: 127.26829268
Subtract 656 from 680 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

In conclusion, the division gives 127.26829268 with a balance of 2.4e-08.