We divide 271663 by 42
We want to figure out the number of times 271663 can be divided by 42.

On to step 1:
If we divide 2 by 42, we get 0 and a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 42

Going ahead to step 2:
The number 42 fits into 27 0 times, leaving a remainder of 27.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 27 leaves us with 27.
Include the next digit (1) from the dividend after 27, then repeat: 271 / 42

Moving on to step 3:
271 divided by 42 is 6 with a remainder of 19.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we take 252 away from 271, we end up with 19.
Fetch the next digit (6) from the dividend, attach it to 19 and continue: 196 / 42

On to step 4:
42 goes into 196 4 times with a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 64.0
Subtracting 168 from 196 leaves us with 28.
Append the next digit (6) from the dividend to 28 and continue with: 286 / 42

Going ahead to step 5:
If we divide 286 by 42, we get 6 and a remainder of 34.
Record the quotient 6 as the next digit in the result. 
Result so far: 646.0
Deduct 252 from 286 and we're left with 34.
Take the next digit (3) from the dividend and append it to 34, then repeat: 343 / 42

On to step 6:
The number 42 fits into 343 8 times, leaving a remainder of 7.
Use 8 as the next digit of our solution. 
Result so far: 6468.0
Subtracting 336 from 343 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 7:
If we divide 70 by 42, we get 1 and a remainder of 28.
Record the quotient 1 as the next digit in the result. 
Result so far: 6468.1
If we subtract 42 from 70, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 8:
If we divide 280 by 42, we get 6 and a remainder of 28.
The next digit of our result is 6. 
Result so far: 6468.16
Subtracting 252 from 280 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 9:
If we divide 280 by 42, we get 6 and a remainder of 28.
Put 6 as the next digit of the answer. 
Result so far: 6468.166
The remainder is 28 after subtracting 252 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

The quotient of the division is 6468.166, and the remainder is 0.0028.