We look at the division of 175971 by 66 
We want to figure out the number of times 175971 can be divided by 66.

Going ahead to step 1:
66 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 66

On to step 2:
If we divide 17 by 66, we get 0 and a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 17 to get 17.
Bring next digit (5) of the dividend behind the 17 and repeat the process: 175 / 66

Advancing to step 3:
66 can be fit into 175 2 times, resulting in a remainder of 43.
The next digit of our result is 2. 
Result so far: 2.0
Subtract 132 from 175 to get 43.
Take the next digit (9) from the dividend and append it to 43, then repeat: 439 / 66

Let's proceed to step 4:
If we divide 439 by 66, we get 6 and a remainder of 43.
Record the quotient 6 as the next digit in the result. 
Result so far: 26.0
If we subtract 396 from 439, we get 43.
Include the next digit (7) from the dividend after 43, then repeat: 437 / 66

Let's proceed to step 5:
If we divide 437 by 66, we get 6 and a remainder of 41.
Use 6 as the next digit of our solution. 
Result so far: 266.0
Deduct 396 from 437 and we're left with 41.
Include the next digit (1) from the dividend after 41, then repeat: 411 / 66

Moving on to step 6:
If we divide 411 by 66, we get 6 and a remainder of 15.
The next digit of our result is 6. 
Result so far: 2666.0
Subtract 396 from 411 to 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.

On to step 7:
If we divide 150 by 66, we get 2 and a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 2666.2
The remainder is 18 after subtracting 132 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 8:
66 can be fit into 180 2 times, resulting in a remainder of 48.
Put 2 as the next digit of the answer. 
Result so far: 2666.22
If we take 132 away from 180, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

After the division, we end up with 2666.22 and a remainder of 0.048.