We look at the division of 8591 by 77 
Let's see how many times 77 fits into 8591.

Advancing to step 1:
When dividing 8 by 77, we get 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 77

Moving on to step 2:
When dividing 85 by 77, we get 1 with a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 77 from 85, we get 8.
Take the next digit (9) from the dividend and append it to 8, then repeat: 89 / 77

Going ahead to step 3:
The number 77 fits into 89 1 times, leaving a remainder of 12.
Write down 1 as next digit of the result. 
Result so far: 11.0
Deduct 77 from 89 and we're left with 12.
Take the next digit (1) from the dividend and append it to 12, then repeat: 121 / 77

Moving on to step 4:
If we divide 121 by 77, we get 1 and a remainder of 44.
Write down 1 as next digit of the result. 
Result so far: 111.0
Subtracting 77 from 121 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Let's proceed to step 5:
77 goes into 440 5 times with a remainder of 55.
The next digit of our result is 5. 
Result so far: 111.5
If we take 385 away from 440, we end up with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 6:
If we divide 550 by 77, we get 7 and a remainder of 11.
The number 7 becomes the next digit in our result. 
Result so far: 111.57
The remainder is 11 after subtracting 539 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 7:
110 divided by 77 is 1 with a remainder of 33.
Put 1 as the next digit of the answer. 
Result so far: 111.571
Deduct 77 from 110 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.

Going ahead to step 8:
330 divided by 77 is 4 with a remainder of 22.
Write down 4 as next digit of the result. 
Result so far: 111.5714
Subtracting 308 from 330 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 9:
77 goes into 220 2 times with a remainder of 66.
Write down 2 as next digit of the result. 
Result so far: 111.57142
The remainder is 66 after subtracting 154 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Advancing to step 10:
660 divided by 77 is 8 with a remainder of 44.
Record the quotient 8 as the next digit in the result. 
Result so far: 111.571428
Subtract 616 from 660 to get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Let's proceed to step 11:
When dividing 440 by 77, we get 5 with a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 111.5714285
Subtracting 385 from 440 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 12:
The number 77 fits into 550 7 times, leaving a remainder of 11.
Record the quotient 7 as the next digit in the result. 
Result so far: 111.57142857
Subtracting 539 from 550 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

In conclusion, the division gives 111.57142857 with a balance of 1.1e-08.