585717 ÷ 66 
Our goal is to divide 585717 by 66.

Step 1:
If we divide 5 by 66, we get 0 and a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 66

Going ahead to step 2:
58 divided by 66 is 0 with a remainder of 58.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 58, we get 58.
Grab the next digit (5) from the dividend, add it to 58, then carry on: 585 / 66

Let's proceed to step 3:
66 goes into 585 8 times with a remainder of 57.
The next digit of our result is 8. 
Result so far: 8.0
Subtracting 528 from 585 leaves us with 57.
Bring next digit (7) of the dividend behind the 57 and repeat the process: 577 / 66

Step 4:
66 goes into 577 8 times with a remainder of 49.
Write down 8 as next digit of the result. 
Result so far: 88.0
Subtract 528 from 577 to get 49.
Fetch the next digit (1) from the dividend, attach it to 49 and continue: 491 / 66

Step 5:
66 goes into 491 7 times with a remainder of 29.
Write down 7 as next digit of the result. 
Result so far: 887.0
Subtracting 462 from 491 leaves us with 29.
Bring next digit (7) of the dividend behind the 29 and repeat the process: 297 / 66

Step 6:
66 goes into 297 4 times with a remainder of 33.
Record the quotient 4 as the next digit in the result. 
Result so far: 8874.0
Deduct 264 from 297 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 7:
330 divided by 66 is 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 8874.5
If we take 330 away from 330, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 8:
66 can be fit into 0 0 times, resulting in a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 8874.5
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 9:
66 goes into 0 0 times with a remainder of 0.
The next digit of our result is 0. 
Result so far: 8874.5
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 8874.5, and the remainder is 0.0.