We're dividing 419813 by 821 
Let's see how many times 821 fits into 419813.

Going ahead to step 1:
When dividing 4 by 821, we get 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 821

Going ahead to step 2:
41 divided by 821 is 0 with a remainder of 41.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 41, we end up with 41.
Include the next digit (9) from the dividend after 41, then repeat: 419 / 821

Advancing to step 3:
821 can be fit into 419 0 times, resulting in a remainder of 419.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 419 leaves us with 419.
Grab the next digit (8) from the dividend, add it to 419, then carry on: 4198 / 821

Going ahead to step 4:
821 goes into 4198 5 times with a remainder of 93.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we take 4105 away from 4198, we end up with 93.
Bring next digit (1) of the dividend behind the 93 and repeat the process: 931 / 821

Step 5:
If we divide 931 by 821, we get 1 and a remainder of 110.
Put 1 as the next digit of the answer. 
Result so far: 51.0
Subtract 821 from 931 to get 110.
Take the next digit (3) from the dividend and append it to 110, then repeat: 1103 / 821

Moving on to step 6:
When dividing 1103 by 821, we get 1 with a remainder of 282.
Record the quotient 1 as the next digit in the result. 
Result so far: 511.0
Subtract 821 from 1103 to get 282.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2820, and continue the process.

On to step 7:
The number 821 fits into 2820 3 times, leaving a remainder of 357.
Put 3 as the next digit of the answer. 
Result so far: 511.3
Subtracting 2463 from 2820 leaves us with 357.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3570, and continue the process.

On to step 8:
The number 821 fits into 3570 4 times, leaving a remainder of 286.
The number 4 becomes the next digit in our result. 
Result so far: 511.34
Subtracting 3284 from 3570 leaves us with 286.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2860, and continue the process.

On to step 9:
821 can be fit into 2860 3 times, resulting in a remainder of 397.
Put 3 as the next digit of the answer. 
Result so far: 511.343
If we take 2463 away from 2860, we end up with 397.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3970, and continue the process.

Advancing to step 10:
821 goes into 3970 4 times with a remainder of 686.
Put 4 as the next digit of the answer. 
Result so far: 511.3434
The remainder is 686 after subtracting 3284 from 3970.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6860, and continue the process.

Moving on to step 11:
When dividing 6860 by 821, we get 8 with a remainder of 292.
Use 8 as the next digit of our solution. 
Result so far: 511.34348
Subtract 6568 from 6860 to get 292.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2920, and continue the process.

Advancing to step 12:
The number 821 fits into 2920 3 times, leaving a remainder of 457.
Use 3 as the next digit of our solution. 
Result so far: 511.343483
If we take 2463 away from 2920, we end up with 457.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4570, and continue the process.

Let's proceed to step 13:
4570 divided by 821 is 5 with a remainder of 465.
Record the quotient 5 as the next digit in the result. 
Result so far: 511.3434835
Subtracting 4105 from 4570 leaves us with 465.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4650, and continue the process.

Moving on to step 14:
4650 divided by 821 is 5 with a remainder of 545.
The next digit of our result is 5. 
Result so far: 511.34348355
If we take 4105 away from 4650, we end up with 545.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5450, and continue the process.

The quotient of the division is 511.34348355, and the remainder is 5.45e-07.