We're dividing 431976 by 66 
Our goal is to divide 431976 by 66.

Moving on to step 1:
When dividing 4 by 66, we get 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 66

Going ahead to step 2:
If we divide 43 by 66, we get 0 and a remainder of 43.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 43, we get 43.
Fetch the next digit (1) from the dividend, attach it to 43 and continue: 431 / 66

Step 3:
If we divide 431 by 66, we get 6 and a remainder of 35.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
The remainder is 35 after subtracting 396 from 431.
Bring next digit (9) of the dividend behind the 35 and repeat the process: 359 / 66

Step 4:
66 goes into 359 5 times with a remainder of 29.
Write down 5 as next digit of the result. 
Result so far: 65.0
Deduct 330 from 359 and we're left with 29.
Include the next digit (7) from the dividend after 29, then repeat: 297 / 66

Going ahead to step 5:
If we divide 297 by 66, we get 4 and a remainder of 33.
Record the quotient 4 as the next digit in the result. 
Result so far: 654.0
The remainder is 33 after subtracting 264 from 297.
Fetch the next digit (6) from the dividend, attach it to 33 and continue: 336 / 66

Going ahead to step 6:
66 can be fit into 336 5 times, resulting in a remainder of 6.
Use 5 as the next digit of our solution. 
Result so far: 6545.0
Subtracting 330 from 336 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 7:
66 goes into 60 0 times with a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 6545.0
If we take 0 away from 60, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Going ahead to step 8:
600 divided by 66 is 9 with a remainder of 6.
Use 9 as the next digit of our solution. 
Result so far: 6545.09
Deduct 594 from 600 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 9:
60 divided by 66 is 0 with a remainder of 60.
Put 0 as the next digit of the answer. 
Result so far: 6545.09
Subtracting 0 from 60 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 10:
The number 66 fits into 600 9 times, leaving a remainder of 6.
The next digit of our result is 9. 
Result so far: 6545.0909
If we take 594 away from 600, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 11:
66 goes into 60 0 times with a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 6545.0909
Deduct 0 from 60 and we're left with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Let's proceed to step 12:
66 goes into 600 9 times with a remainder of 6.
The next digit of our result is 9. 
Result so far: 6545.090909
If we take 594 away from 600, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 13:
If we divide 60 by 66, we get 0 and a remainder of 60.
Record the quotient 0 as the next digit in the result. 
Result so far: 6545.090909
Subtracting 0 from 60 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Let's proceed to step 14:
600 divided by 66 is 9 with a remainder of 6.
Use 9 as the next digit of our solution. 
Result so far: 6545.09090909
The remainder is 6 after subtracting 594 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final result is 6545.09090909 with a remainder of 6e-09.