We look at the division of 827824 by 82 
We're looking to find how many times 82 goes into 827824.

Step 1:
When dividing 8 by 82, we get 0 with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Include the next digit (2) from the dividend after 8, then repeat: 82 / 82

On to step 2:
The number 82 fits into 82 1 times, leaving a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 82 away from 82, we end up with 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 82

Let's proceed to step 3:
When dividing 7 by 82, we get 0 with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 10.0
If we take 0 away from 7, we end up with 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 82

Advancing to step 4:
82 can be fit into 78 0 times, resulting in a remainder of 78.
The number 0 becomes the next digit in our result. 
Result so far: 100.0
The remainder is 78 after subtracting 0 from 78.
Fetch the next digit (2) from the dividend, attach it to 78 and continue: 782 / 82

On to step 5:
782 divided by 82 is 9 with a remainder of 44.
The next digit of our result is 9. 
Result so far: 1009.0
If we take 738 away from 782, we end up with 44.
Fetch the next digit (4) from the dividend, attach it to 44 and continue: 444 / 82

Advancing to step 6:
82 can be fit into 444 5 times, resulting in a remainder of 34.
The number 5 becomes the next digit in our result. 
Result so far: 10095.0
If we subtract 410 from 444, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Let's proceed to step 7:
82 goes into 340 4 times with a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 10095.4
The remainder is 12 after subtracting 328 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 8:
The number 82 fits into 120 1 times, leaving a remainder of 38.
Put 1 as the next digit of the answer. 
Result so far: 10095.41
Subtract 82 from 120 to get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Step 9:
82 goes into 380 4 times with a remainder of 52.
The number 4 becomes the next digit in our result. 
Result so far: 10095.414
If we subtract 328 from 380, we get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 10:
82 goes into 520 6 times with a remainder of 28.
Record the quotient 6 as the next digit in the result. 
Result so far: 10095.4146
If we subtract 492 from 520, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 11:
82 can be fit into 280 3 times, resulting in a remainder of 34.
Write down 3 as next digit of the result. 
Result so far: 10095.41463
Deduct 246 from 280 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 12:
82 goes into 340 4 times with a remainder of 12.
The next digit of our result is 4. 
Result so far: 10095.414634
Subtracting 328 from 340 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 13:
82 can be fit into 120 1 times, resulting in a remainder of 38.
Put 1 as the next digit of the answer. 
Result so far: 10095.4146341
If we take 82 away from 120, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 14:
82 goes into 380 4 times with a remainder of 52.
Write down 4 as next digit of the result. 
Result so far: 10095.41463414
The remainder is 52 after subtracting 328 from 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

After the division, we end up with 10095.41463414 and a remainder of 5.2e-08.