421713 ÷ 82 
We're looking to find how many times 82 goes into 421713.

Going ahead to step 1:
4 divided by 82 is 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 82

Step 2:
The number 82 fits into 42 0 times, leaving a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 42 after subtracting 0 from 42.
Append the next digit (1) from the dividend to 42 and continue with: 421 / 82

On to step 3:
If we divide 421 by 82, we get 5 and a remainder of 11.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtract 410 from 421 to get 11.
Include the next digit (7) from the dividend after 11, then repeat: 117 / 82

Let's proceed to step 4:
When dividing 117 by 82, we get 1 with a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 51.0
Subtracting 82 from 117 leaves us with 35.
Take the next digit (1) from the dividend and append it to 35, then repeat: 351 / 82

On to step 5:
When dividing 351 by 82, we get 4 with a remainder of 23.
The number 4 becomes the next digit in our result. 
Result so far: 514.0
If we subtract 328 from 351, we get 23.
Append the next digit (3) from the dividend to 23 and continue with: 233 / 82

Advancing to step 6:
82 can be fit into 233 2 times, resulting in a remainder of 69.
The next digit of our result is 2. 
Result so far: 5142.0
The remainder is 69 after subtracting 164 from 233.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Going ahead to step 7:
690 divided by 82 is 8 with a remainder of 34.
The next digit of our result is 8. 
Result so far: 5142.8
Deduct 656 from 690 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.

Let's proceed to step 8:
82 goes into 340 4 times with a remainder of 12.
The next digit of our result is 4. 
Result so far: 5142.84
If we take 328 away from 340, we end up 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.

Let's proceed to step 9:
When dividing 120 by 82, we get 1 with a remainder of 38.
The next digit of our result is 1. 
Result so far: 5142.841
The remainder is 38 after subtracting 82 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Going ahead to step 10:
82 can be fit into 380 4 times, resulting in a remainder of 52.
Write down 4 as next digit of the result. 
Result so far: 5142.8414
Subtracting 328 from 380 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Let's proceed to step 11:
If we divide 520 by 82, we get 6 and a remainder of 28.
Put 6 as the next digit of the answer. 
Result so far: 5142.84146
If we take 492 away from 520, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 12:
If we divide 280 by 82, we get 3 and a remainder of 34.
Write down 3 as next digit of the result. 
Result so far: 5142.841463
The remainder is 34 after subtracting 246 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 13:
When dividing 340 by 82, we get 4 with a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 5142.8414634
Subtract 328 from 340 to get 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 14:
If we divide 120 by 82, we get 1 and a remainder of 38.
Write down 1 as next digit of the result. 
Result so far: 5142.84146341
Subtracting 82 from 120 leaves us 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.

After the division, we end up with 5142.84146341 and a remainder of 3.8e-08.