We're dividing 821021 by 53 
We want to divide 821021 by 53.

On to step 1:
The number 53 fits into 8 0 times, leaving a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Fetch the next digit (2) from the dividend, attach it to 8 and continue: 82 / 53

Going ahead to step 2:
If we divide 82 by 53, we get 1 and a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 29 after subtracting 53 from 82.
Take the next digit (1) from the dividend and append it to 29, then repeat: 291 / 53

On to step 3:
If we divide 291 by 53, we get 5 and a remainder of 26.
The number 5 becomes the next digit in our result. 
Result so far: 15.0
If we take 265 away from 291, we end up with 26.
Take the next digit (0) from the dividend and append it to 26, then repeat: 260 / 53

Advancing to step 4:
53 goes into 260 4 times with a remainder of 48.
Write down 4 as next digit of the result. 
Result so far: 154.0
If we subtract 212 from 260, we get 48.
Fetch the next digit (2) from the dividend, attach it to 48 and continue: 482 / 53

On to step 5:
53 can be fit into 482 9 times, resulting in a remainder of 5.
Write down 9 as next digit of the result. 
Result so far: 1549.0
If we take 477 away from 482, we end up with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 53

Advancing to step 6:
If we divide 51 by 53, we get 0 and a remainder of 51.
Put 0 as the next digit of the answer. 
Result so far: 15490.0
If we take 0 away from 51, we end up with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Going ahead to step 7:
The number 53 fits into 510 9 times, leaving a remainder of 33.
Use 9 as the next digit of our solution. 
Result so far: 15490.9
If we take 477 away from 510, we end up with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Let's proceed to step 8:
53 can be fit into 330 6 times, resulting in a remainder of 12.
The next digit of our result is 6. 
Result so far: 15490.96
Subtract 318 from 330 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 9:
When dividing 120 by 53, we get 2 with a remainder of 14.
Use 2 as the next digit of our solution. 
Result so far: 15490.962
If we subtract 106 from 120, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 10:
The number 53 fits into 140 2 times, leaving a remainder of 34.
Record the quotient 2 as the next digit in the result. 
Result so far: 15490.9622
The remainder is 34 after subtracting 106 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

The quotient of the division is 15490.9622, and the remainder is 0.00034.