Let's divide 263909 by 42
Our goal is to divide 263909 by 42.

On to step 1:
If we divide 2 by 42, we get 0 and a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 42

On to step 2:
If we divide 26 by 42, we get 0 and a remainder of 26.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 26 to get 26.
Append the next digit (3) from the dividend to 26 and continue with: 263 / 42

Moving on to step 3:
263 divided by 42 is 6 with a remainder of 11.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 11 after subtracting 252 from 263.
Fetch the next digit (9) from the dividend, attach it to 11 and continue: 119 / 42

On to step 4:
The number 42 fits into 119 2 times, leaving a remainder of 35.
The next digit of our result is 2. 
Result so far: 62.0
If we subtract 84 from 119, we get 35.
Include the next digit (0) from the dividend after 35, then repeat: 350 / 42

Moving on to step 5:
If we divide 350 by 42, we get 8 and a remainder of 14.
Write down 8 as next digit of the result. 
Result so far: 628.0
Subtract 336 from 350 to get 14.
Bring next digit (9) of the dividend behind the 14 and repeat the process: 149 / 42

Advancing to step 6:
42 goes into 149 3 times with a remainder of 23.
Write down 3 as next digit of the result. 
Result so far: 6283.0
If we take 126 away from 149, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

On to step 7:
The number 42 fits into 230 5 times, leaving a remainder of 20.
Record the quotient 5 as the next digit in the result. 
Result so far: 6283.5
The remainder is 20 after subtracting 210 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
200 divided by 42 is 4 with a remainder of 32.
Record the quotient 4 as the next digit in the result. 
Result so far: 6283.54
The remainder is 32 after subtracting 168 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 9:
The number 42 fits into 320 7 times, leaving a remainder of 26.
The next digit of our result is 7. 
Result so far: 6283.547
Subtracting 294 from 320 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 10:
When dividing 260 by 42, we get 6 with a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 6283.5476
If we subtract 252 from 260, we get 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:
42 goes into 80 1 times with a remainder of 38.
The number 1 becomes the next digit in our result. 
Result so far: 6283.54761
The remainder is 38 after subtracting 42 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Going ahead to step 12:
380 divided by 42 is 9 with a remainder of 2.
The number 9 becomes the next digit in our result. 
Result so far: 6283.547619
If we subtract 378 from 380, we 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.

Step 13:
42 can be fit into 20 0 times, resulting in a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 6283.547619
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.

Let's proceed to step 14:
42 goes into 200 4 times with a remainder of 32.
Use 4 as the next digit of our solution. 
Result so far: 6283.54761904
Deduct 168 from 200 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

After the division, we end up with 6283.54761904 and a remainder of 3.2e-08.