414735 ÷ 21 
We want to figure out the number of times 414735 can be divided by 21.

On to step 1:
The number 21 fits into 4 0 times, leaving a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Fetch the next digit (1) from the dividend, attach it to 4 and continue: 41 / 21

Moving on to step 2:
21 can be fit into 41 1 times, resulting in a remainder of 20.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 21 from 41 leaves us with 20.
Bring next digit (4) of the dividend behind the 20 and repeat the process: 204 / 21

Moving on to step 3:
When dividing 204 by 21, we get 9 with a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 19.0
Subtracting 189 from 204 leaves us with 15.
Take the next digit (7) from the dividend and append it to 15, then repeat: 157 / 21

Advancing to step 4:
The number 21 fits into 157 7 times, leaving a remainder of 10.
Use 7 as the next digit of our solution. 
Result so far: 197.0
If we subtract 147 from 157, we get 10.
Fetch the next digit (3) from the dividend, attach it to 10 and continue: 103 / 21

Step 5:
103 divided by 21 is 4 with a remainder of 19.
Write down 4 as next digit of the result. 
Result so far: 1974.0
Subtract 84 from 103 to get 19.
Include the next digit (5) from the dividend after 19, then repeat: 195 / 21

Let's proceed to step 6:
21 goes into 195 9 times with a remainder of 6.
Write down 9 as next digit of the result. 
Result so far: 19749.0
Deduct 189 from 195 and we're left 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.

Advancing to step 7:
When dividing 60 by 21, we get 2 with a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 19749.2
Deduct 42 from 60 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 8:
21 can be fit into 180 8 times, resulting in a remainder of 12.
The next digit of our result is 8. 
Result so far: 19749.28
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.

Going ahead to step 9:
The number 21 fits into 120 5 times, leaving a remainder of 15.
The next digit of our result is 5. 
Result so far: 19749.285
The remainder is 15 after subtracting 105 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 10:
If we divide 150 by 21, we get 7 and a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 19749.2857
Subtract 147 from 150 to 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.

On to step 11:
The number 21 fits into 30 1 times, leaving a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 19749.28571
Subtract 21 from 30 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 12:
When dividing 90 by 21, we get 4 with a remainder of 6.
The next digit of our result is 4. 
Result so far: 19749.285714
The remainder is 6 after subtracting 84 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 13:
21 can be fit into 60 2 times, resulting in a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 19749.2857142
Deduct 42 from 60 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 14:
21 can be fit into 180 8 times, resulting in a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 19749.28571428
Subtract 168 from 180 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.

Our division results in 19749.28571428 with a remaining 1.2e-08.