We look at the division of 635874 by 21 
We want to divide 635874 by 21.

Going ahead to step 1:
21 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 21

Step 2:
21 goes into 63 3 times with a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Deduct 63 from 63 and we're left with 0.
Append the next digit (5) from the dividend to 0 and continue with: 5 / 21

Advancing to step 3:
If we divide 5 by 21, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 30.0
If we take 0 away from 5, we end up with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 21

On to step 4:
21 can be fit into 58 2 times, resulting in a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 302.0
If we take 42 away from 58, we end up with 16.
Bring next digit (7) of the dividend behind the 16 and repeat the process: 167 / 21

Moving on to step 5:
If we divide 167 by 21, we get 7 and a remainder of 20.
The number 7 becomes the next digit in our result. 
Result so far: 3027.0
If we take 147 away from 167, we end up with 20.
Fetch the next digit (4) from the dividend, attach it to 20 and continue: 204 / 21

Let's proceed to step 6:
The number 21 fits into 204 9 times, leaving a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 30279.0
If we subtract 189 from 204, we 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 7:
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: 30279.7
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.

Step 8:
If we divide 30 by 21, we get 1 and a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 30279.71
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.

Step 9:
21 goes into 90 4 times with a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 30279.714
Subtract 84 from 90 to get 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 10:
21 can be fit into 60 2 times, resulting in a remainder of 18.
Put 2 as the next digit of the answer. 
Result so far: 30279.7142
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.

Step 11:
The number 21 fits into 180 8 times, leaving a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 30279.71428
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.

Going ahead to step 12:
21 can be fit into 120 5 times, resulting in a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 30279.714285
If we subtract 105 from 120, we 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 13:
21 can be fit into 150 7 times, resulting in a remainder of 3.
The next digit of our result is 7. 
Result so far: 30279.7142857
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.

Advancing to step 14:
21 goes into 30 1 times with a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 30279.71428571
Deduct 21 from 30 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

The final result is 30279.71428571 with a remainder of 9e-09.