We're dividing 419970 by 21 
We're looking to find how many times 21 goes into 419970.

Advancing to step 1:
4 divided by 21 is 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 21

Going ahead to step 2:
When dividing 41 by 21, we get 1 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.
Include the next digit (9) from the dividend after 20, then repeat: 209 / 21

Let's proceed to step 3:
The number 21 fits into 209 9 times, leaving a remainder of 20.
Record the quotient 9 as the next digit in the result. 
Result so far: 19.0
The remainder is 20 after subtracting 189 from 209.
Append the next digit (9) from the dividend to 20 and continue with: 209 / 21

On to step 4:
209 divided by 21 is 9 with a remainder of 20.
The number 9 becomes the next digit in our result. 
Result so far: 199.0
Subtract 189 from 209 to get 20.
Bring next digit (7) of the dividend behind the 20 and repeat the process: 207 / 21

Step 5:
The number 21 fits into 207 9 times, leaving a remainder of 18.
The number 9 becomes the next digit in our result. 
Result so far: 1999.0
Deduct 189 from 207 and we're left with 18.
Bring next digit (0) of the dividend behind the 18 and repeat the process: 180 / 21

Let's proceed to step 6:
The number 21 fits into 180 8 times, leaving a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 19998.0
Deduct 168 from 180 and we're left 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.

Step 7:
21 goes into 120 5 times with a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 19998.5
Deduct 105 from 120 and we're left 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.

Step 8:
21 can be fit into 150 7 times, resulting in a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 19998.57
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 9:
30 divided by 21 is 1 with a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 19998.571
If we subtract 21 from 30, we 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.

Let's proceed to step 10:
90 divided by 21 is 4 with a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 19998.5714
Deduct 84 from 90 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.

Moving on to step 11:
21 can be fit into 60 2 times, resulting in a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 19998.57142
If we take 42 away from 60, we end up 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.

On to step 12:
If we divide 180 by 21, we get 8 and a remainder of 12.
The next digit of our result is 8. 
Result so far: 19998.571428
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.

Advancing to step 13:
120 divided by 21 is 5 with a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 19998.5714285
Subtract 105 from 120 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 14:
When dividing 150 by 21, we get 7 with a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 19998.57142857
The remainder is 3 after subtracting 147 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The quotient of the division is 19998.57142857, and the remainder is 3e-09.