We look at the division of 271663 by 6 
Let's see how many times 6 fits into 271663.

Step 1:
When dividing 2 by 6, we get 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Take the next digit (7) from the dividend and append it to 2, then repeat: 27 / 6

Advancing to step 2:
When dividing 27 by 6, we get 4 with a remainder of 3.
Write down 4 as next digit of the result. 
Result so far: 4.0
Subtracting 24 from 27 leaves us with 3.
Append the next digit (1) from the dividend to 3 and continue with: 31 / 6

Step 3:
6 can be fit into 31 5 times, resulting in a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 45.0
If we take 30 away from 31, we end up with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 6

Going ahead to step 4:
6 can be fit into 16 2 times, resulting in a remainder of 4.
The next digit of our result is 2. 
Result so far: 452.0
Subtract 12 from 16 to get 4.
Fetch the next digit (6) from the dividend, attach it to 4 and continue: 46 / 6

Let's proceed to step 5:
If we divide 46 by 6, we get 7 and a remainder of 4.
The next digit of our result is 7. 
Result so far: 4527.0
Subtracting 42 from 46 leaves us with 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 6

Advancing to step 6:
If we divide 43 by 6, we get 7 and a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 45277.0
If we subtract 42 from 43, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
The number 6 fits into 10 1 times, leaving a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 45277.1
If we take 6 away from 10, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 8:
If we divide 40 by 6, we get 6 and a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 45277.16
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
If we divide 40 by 6, we get 6 and a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 45277.166
If we subtract 36 from 40, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 45277.166, and the remainder is 0.0004.