We're dividing 666009 by 9 
We're looking to find how many times 9 goes into 666009.

Step 1:
When dividing 6 by 9, we get 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 9

Moving on to step 2:
The number 9 fits into 66 7 times, leaving a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Deduct 63 from 66 and we're left with 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 9

Step 3:
9 goes into 36 4 times with a remainder of 0.
The number 4 becomes the next digit in our result. 
Result so far: 74.0
Subtract 36 from 36 to get 0.
Fetch the next digit (0) from the dividend, attach it to 0 and continue: 0 / 9

On to step 4:
0 divided by 9 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 740.0
The remainder is 0 after subtracting 0 from 0.
Include the next digit (0) from the dividend after 0, then repeat: 0 / 9

Advancing to step 5:
When dividing 0 by 9, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 7400.0
If we subtract 0 from 0, we get 0.
Fetch the next digit (9) from the dividend, attach it to 0 and continue: 9 / 9

Going ahead to step 6:
9 goes into 9 1 times with a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 74001.0
If we subtract 9 from 9, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 7:
0 divided by 9 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 74001.0
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.

Advancing to step 8:
If we divide 0 by 9, we get 0 and a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 74001.0
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 74001.0, and the remainder is 0.0.