Let's divide 414105 by 21
Our goal is to divide 414105 by 21.

Advancing to step 1:
When dividing 4 by 21, we get 0 with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 21

Moving on to step 2:
21 goes into 41 1 times with a remainder of 20.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 21 from 41 leaves us with 20.
Append the next digit (4) from the dividend to 20 and continue with: 204 / 21

Step 3:
When dividing 204 by 21, we get 9 with a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 19.0
The remainder is 15 after subtracting 189 from 204.
Include the next digit (1) from the dividend after 15, then repeat: 151 / 21

Moving on to step 4:
21 can be fit into 151 7 times, resulting in a remainder of 4.
Put 7 as the next digit of the answer. 
Result so far: 197.0
Subtract 147 from 151 to get 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 21

Let's proceed to step 5:
21 goes into 40 1 times with a remainder of 19.
Write down 1 as next digit of the result. 
Result so far: 1971.0
Subtracting 21 from 40 leaves us with 19.
Grab the next digit (5) from the dividend, add it to 19, then carry on: 195 / 21

Advancing to step 6:
The number 21 fits into 195 9 times, leaving a remainder of 6.
The number 9 becomes the next digit in our result. 
Result so far: 19719.0
If we take 189 away from 195, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 7:
When dividing 60 by 21, we get 2 with a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 19719.2
The remainder is 18 after subtracting 42 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 8:
21 goes into 180 8 times with a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 19719.28
The remainder is 12 after subtracting 168 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 9:
When dividing 120 by 21, we get 5 with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 19719.285
Subtracting 105 from 120 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 10:
21 goes into 150 7 times with a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 19719.2857
If we subtract 147 from 150, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 11:
21 can be fit into 30 1 times, resulting in a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 19719.28571
The remainder is 9 after subtracting 21 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 12:
21 can be fit into 90 4 times, resulting in a remainder of 6.
The next digit of our result is 4. 
Result so far: 19719.285714
Subtracting 84 from 90 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 13:
The number 21 fits into 60 2 times, leaving a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 19719.2857142
Subtract 42 from 60 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 14:
When dividing 180 by 21, we get 8 with a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 19719.28571428
If we take 168 away from 180, 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.

The quotient of the division is 19719.28571428, and the remainder is 1.2e-08.