We look at the division of 413114 by 21 
Let's see how many times 21 fits into 413114.

Step 1:
If we divide 4 by 21, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 21

On to step 2:
21 goes into 41 1 times with a remainder of 20.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 20 after subtracting 21 from 41.
Include the next digit (3) from the dividend after 20, then repeat: 203 / 21

Moving on to step 3:
21 can be fit into 203 9 times, resulting in a remainder of 14.
The next digit of our result is 9. 
Result so far: 19.0
If we subtract 189 from 203, we get 14.
Grab the next digit (1) from the dividend, add it to 14, then carry on: 141 / 21

Let's proceed to step 4:
21 can be fit into 141 6 times, resulting in a remainder of 15.
The next digit of our result is 6. 
Result so far: 196.0
If we subtract 126 from 141, we get 15.
Fetch the next digit (1) from the dividend, attach it to 15 and continue: 151 / 21

Let's proceed to step 5:
21 goes into 151 7 times with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 1967.0
The remainder is 4 after subtracting 147 from 151.
Take the next digit (4) from the dividend and append it to 4, then repeat: 44 / 21

Moving on to step 6:
21 goes into 44 2 times with a remainder of 2.
The next digit of our result is 2. 
Result so far: 19672.0
Subtract 42 from 44 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 7:
If we divide 20 by 21, we get 0 and a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 19672.0
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 8:
If we divide 200 by 21, we get 9 and a remainder of 11.
Write down 9 as next digit of the result. 
Result so far: 19672.09
Deduct 189 from 200 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 9:
21 can be fit into 110 5 times, resulting in a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 19672.095
Deduct 105 from 110 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 10:
If we divide 50 by 21, we get 2 and a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 19672.0952
Deduct 42 from 50 and we're left 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.

Advancing to step 11:
If we divide 80 by 21, we get 3 and a remainder of 17.
The number 3 becomes the next digit in our result. 
Result so far: 19672.09523
If we take 63 away from 80, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

On to step 12:
When dividing 170 by 21, we get 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 19672.095238
Subtract 168 from 170 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 13:
When dividing 20 by 21, we get 0 with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 19672.095238
If we subtract 0 from 20, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 14:
If we divide 200 by 21, we get 9 and a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 19672.09523809
If we subtract 189 from 200, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Our division results in 19672.09523809 with a remaining 1.1e-08.