We're dividing 661577 by 9 
Our goal is to divide 661577 by 9.

On to step 1:
The number 9 fits into 6 0 times, leaving a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 9

On to step 2:
If we divide 66 by 9, we get 7 and a remainder of 3.
The next digit of our result is 7. 
Result so far: 7.0
Subtract 63 from 66 to get 3.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 9

Advancing to step 3:
When dividing 31 by 9, we get 3 with a remainder of 4.
The number 3 becomes the next digit in our result. 
Result so far: 73.0
Subtract 27 from 31 to get 4.
Grab the next digit (5) from the dividend, add it to 4, then carry on: 45 / 9

Let's proceed to step 4:
9 goes into 45 5 times with a remainder of 0.
The next digit of our result is 5. 
Result so far: 735.0
If we subtract 45 from 45, we get 0.
Grab the next digit (7) from the dividend, add it to 0, then carry on: 7 / 9

Step 5:
7 divided by 9 is 0 with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 7350.0
Deduct 0 from 7 and we're left with 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 9

Step 6:
9 goes into 77 8 times with a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 73508.0
If we take 72 away from 77, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 7:
If we divide 50 by 9, we get 5 and a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 73508.5
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 8:
When dividing 50 by 9, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 73508.55
Deduct 45 from 50 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final result is 73508.55 with a remainder of 0.005.