We look at the division of 577725 by 77 
Let's see how many times 77 fits into 577725.

Going ahead to step 1:
5 divided by 77 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 77

Step 2:
If we divide 57 by 77, we get 0 and a remainder of 57.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 57 after subtracting 0 from 57.
Take the next digit (7) from the dividend and append it to 57, then repeat: 577 / 77

Moving on to step 3:
577 divided by 77 is 7 with a remainder of 38.
Write down 7 as next digit of the result. 
Result so far: 7.0
If we subtract 539 from 577, we get 38.
Append the next digit (7) from the dividend to 38 and continue with: 387 / 77

Let's proceed to step 4:
77 can be fit into 387 5 times, resulting in a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 75.0
If we subtract 385 from 387, we get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 77

Step 5:
When dividing 22 by 77, we get 0 with a remainder of 22.
The next digit of our result is 0. 
Result so far: 750.0
Subtracting 0 from 22 leaves us with 22.
Fetch the next digit (5) from the dividend, attach it to 22 and continue: 225 / 77

On to step 6:
77 can be fit into 225 2 times, resulting in a remainder of 71.
The next digit of our result is 2. 
Result so far: 7502.0
Subtracting 154 from 225 leaves us with 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Step 7:
710 divided by 77 is 9 with a remainder of 17.
The next digit of our result is 9. 
Result so far: 7502.9
If we subtract 693 from 710, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

On to step 8:
77 can be fit into 170 2 times, resulting in a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 7502.92
Subtract 154 from 170 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 9:
77 can be fit into 160 2 times, resulting in a remainder of 6.
The next digit of our result is 2. 
Result so far: 7502.922
Deduct 154 from 160 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 7502.922 and a remainder of 0.0006.