We're dividing 777706 by 9 
Our goal is to divide 777706 by 9.

Moving on to step 1:
When dividing 7 by 9, we get 0 with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 9

Step 2:
9 can be fit into 77 8 times, resulting in a remainder of 5.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
If we take 72 away from 77, we end up with 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 9

Moving on to step 3:
9 can be fit into 57 6 times, resulting in a remainder of 3.
Use 6 as the next digit of our solution. 
Result so far: 86.0
Deduct 54 from 57 and we're left with 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 9

Advancing to step 4:
9 can be fit into 37 4 times, resulting in a remainder of 1.
The number 4 becomes the next digit in our result. 
Result so far: 864.0
The remainder is 1 after subtracting 36 from 37.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 9

Step 5:
9 can be fit into 10 1 times, resulting in a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 8641.0
Deduct 9 from 10 and we're left with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 9

Advancing to step 6:
If we divide 16 by 9, we get 1 and a remainder of 7.
The next digit of our result is 1. 
Result so far: 86411.0
If we subtract 9 from 16, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
9 goes into 70 7 times with a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 86411.7
Subtracting 63 from 70 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 8:
70 divided by 9 is 7 with a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 86411.77
Subtracting 63 from 70 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The quotient of the division is 86411.77, and the remainder is 0.007.