103271 ÷ 66 
Our goal is to divide 103271 by 66.

Step 1:
When dividing 1 by 66, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 66

On to step 2:
66 can be fit into 10 0 times, resulting in a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Fetch the next digit (3) from the dividend, attach it to 10 and continue: 103 / 66

Going ahead to step 3:
If we divide 103 by 66, we get 1 and a remainder of 37.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 66 from 103 to get 37.
Append the next digit (2) from the dividend to 37 and continue with: 372 / 66

Let's proceed to step 4:
The number 66 fits into 372 5 times, leaving a remainder of 42.
Use 5 as the next digit of our solution. 
Result so far: 15.0
If we subtract 330 from 372, we get 42.
Grab the next digit (7) from the dividend, add it to 42, then carry on: 427 / 66

Step 5:
427 divided by 66 is 6 with a remainder of 31.
Record the quotient 6 as the next digit in the result. 
Result so far: 156.0
If we subtract 396 from 427, we get 31.
Bring next digit (1) of the dividend behind the 31 and repeat the process: 311 / 66

Step 6:
The number 66 fits into 311 4 times, leaving a remainder of 47.
Use 4 as the next digit of our solution. 
Result so far: 1564.0
Subtract 264 from 311 to get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Going ahead to step 7:
If we divide 470 by 66, we get 7 and a remainder of 8.
Record the quotient 7 as the next digit in the result. 
Result so far: 1564.7
If we take 462 away from 470, we end up with 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 8:
66 goes into 80 1 times with a remainder of 14.
Record the quotient 1 as the next digit in the result. 
Result so far: 1564.71
Subtract 66 from 80 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 9:
140 divided by 66 is 2 with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 1564.712
If we take 132 away from 140, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 10:
The number 66 fits into 80 1 times, leaving a remainder of 14.
The next digit of our result is 1. 
Result so far: 1564.7121
The remainder is 14 after subtracting 66 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 11:
The number 66 fits into 140 2 times, leaving a remainder of 8.
The next digit of our result is 2. 
Result so far: 1564.71212
The remainder is 8 after subtracting 132 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 12:
If we divide 80 by 66, we get 1 and a remainder of 14.
Record the quotient 1 as the next digit in the result. 
Result so far: 1564.712121
Subtracting 66 from 80 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 13:
66 can be fit into 140 2 times, resulting in a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 1564.7121212
If we subtract 132 from 140, 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.

Moving on to step 14:
When dividing 80 by 66, we get 1 with a remainder of 14.
The next digit of our result is 1. 
Result so far: 1564.71212121
If we subtract 66 from 80, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

After the division, we end up with 1564.71212121 and a remainder of 1.4e-08.