We look at the division of 584312 by 82 
We want to divide 584312 by 82.

On to step 1:
82 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 82

Advancing to step 2:
If we divide 58 by 82, we get 0 and a remainder of 58.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 58 leaves us with 58.
Bring next digit (4) of the dividend behind the 58 and repeat the process: 584 / 82

Advancing to step 3:
82 goes into 584 7 times with a remainder of 10.
Write down 7 as next digit of the result. 
Result so far: 7.0
If we subtract 574 from 584, we get 10.
Append the next digit (3) from the dividend to 10 and continue with: 103 / 82

Moving on to step 4:
If we divide 103 by 82, we get 1 and a remainder of 21.
Record the quotient 1 as the next digit in the result. 
Result so far: 71.0
If we subtract 82 from 103, we get 21.
Include the next digit (1) from the dividend after 21, then repeat: 211 / 82

Advancing to step 5:
211 divided by 82 is 2 with a remainder of 47.
The next digit of our result is 2. 
Result so far: 712.0
Deduct 164 from 211 and we're left with 47.
Fetch the next digit (2) from the dividend, attach it to 47 and continue: 472 / 82

Advancing to step 6:
When dividing 472 by 82, we get 5 with a remainder of 62.
The number 5 becomes the next digit in our result. 
Result so far: 7125.0
The remainder is 62 after subtracting 410 from 472.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 7:
When dividing 620 by 82, we get 7 with a remainder of 46.
Use 7 as the next digit of our solution. 
Result so far: 7125.7
If we take 574 away from 620, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 8:
460 divided by 82 is 5 with a remainder of 50.
Use 5 as the next digit of our solution. 
Result so far: 7125.75
Subtract 410 from 460 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 9:
When dividing 500 by 82, we get 6 with a remainder of 8.
The next digit of our result is 6. 
Result so far: 7125.756
If we subtract 492 from 500, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 10:
The number 82 fits into 80 0 times, leaving a remainder of 80.
Record the quotient 0 as the next digit in the result. 
Result so far: 7125.756
The remainder is 80 after subtracting 0 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Let's proceed to step 11:
When dividing 800 by 82, we get 9 with a remainder of 62.
Use 9 as the next digit of our solution. 
Result so far: 7125.75609
Subtracting 738 from 800 leaves us with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Advancing to step 12:
82 can be fit into 620 7 times, resulting in a remainder of 46.
Use 7 as the next digit of our solution. 
Result so far: 7125.756097
Subtract 574 from 620 to get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 13:
82 goes into 460 5 times with a remainder of 50.
Write down 5 as next digit of the result. 
Result so far: 7125.7560975
Subtracting 410 from 460 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 14:
82 goes into 500 6 times with a remainder of 8.
The next digit of our result is 6. 
Result so far: 7125.75609756
Subtracting 492 from 500 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The final result is 7125.75609756 with a remainder of 8e-09.