We look at the division of 566974 by 66 
Let's see how many times 66 fits into 566974.

On to step 1:
66 goes into 5 0 times with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 66

Going ahead to step 2:
66 goes into 56 0 times with a remainder of 56.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 56, we get 56.
Take the next digit (6) from the dividend and append it to 56, then repeat: 566 / 66

Going ahead to step 3:
If we divide 566 by 66, we get 8 and a remainder of 38.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Subtract 528 from 566 to get 38.
Append the next digit (9) from the dividend to 38 and continue with: 389 / 66

On to step 4:
If we divide 389 by 66, we get 5 and a remainder of 59.
The next digit of our result is 5. 
Result so far: 85.0
Subtracting 330 from 389 leaves us with 59.
Grab the next digit (7) from the dividend, add it to 59, then carry on: 597 / 66

On to step 5:
66 goes into 597 9 times with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 859.0
If we subtract 594 from 597, we get 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 66

On to step 6:
66 can be fit into 34 0 times, resulting in a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 8590.0
If we subtract 0 from 34, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 7:
66 can be fit into 340 5 times, resulting in a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 8590.5
Subtracting 330 from 340 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 8:
When dividing 100 by 66, we get 1 with a remainder of 34.
Use 1 as the next digit of our solution. 
Result so far: 8590.51
The remainder is 34 after subtracting 66 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 9:
When dividing 340 by 66, we get 5 with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 8590.515
Subtract 330 from 340 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 10:
When dividing 100 by 66, we get 1 with a remainder of 34.
Put 1 as the next digit of the answer. 
Result so far: 8590.5151
Subtract 66 from 100 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 11:
66 can be fit into 340 5 times, resulting in a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 8590.51515
Subtract 330 from 340 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 12:
100 divided by 66 is 1 with a remainder of 34.
Write down 1 as next digit of the result. 
Result so far: 8590.515151
Subtract 66 from 100 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 13:
When dividing 340 by 66, we get 5 with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 8590.5151515
The remainder is 10 after subtracting 330 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 14:
The number 66 fits into 100 1 times, leaving a remainder of 34.
The next digit of our result is 1. 
Result so far: 8590.51515151
If we subtract 66 from 100, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

The final result is 8590.51515151 with a remainder of 3.4e-08.