76657 ÷ 89 
We want to figure out the number of times 76657 can be divided by 89.

Step 1:
89 goes into 7 0 times with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Append the next digit (6) from the dividend to 7 and continue with: 76 / 89

Step 2:
89 can be fit into 76 0 times, resulting in a remainder of 76.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 76, we get 76.
Bring next digit (6) of the dividend behind the 76 and repeat the process: 766 / 89

Let's proceed to step 3:
89 can be fit into 766 8 times, resulting in a remainder of 54.
Write down 8 as next digit of the result. 
Result so far: 8.0
Subtracting 712 from 766 leaves us with 54.
Bring next digit (5) of the dividend behind the 54 and repeat the process: 545 / 89

Moving on to step 4:
If we divide 545 by 89, we get 6 and a remainder of 11.
The number 6 becomes the next digit in our result. 
Result so far: 86.0
The remainder is 11 after subtracting 534 from 545.
Bring next digit (7) of the dividend behind the 11 and repeat the process: 117 / 89

Advancing to step 5:
89 goes into 117 1 times with a remainder of 28.
The number 1 becomes the next digit in our result. 
Result so far: 861.0
The remainder is 28 after subtracting 89 from 117.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 6:
89 can be fit into 280 3 times, resulting in a remainder of 13.
Record the quotient 3 as the next digit in the result. 
Result so far: 861.3
If we take 267 away from 280, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 7:
When dividing 130 by 89, we get 1 with a remainder of 41.
The next digit of our result is 1. 
Result so far: 861.31
Deduct 89 from 130 and we're left with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Going ahead to step 8:
89 can be fit into 410 4 times, resulting in a remainder of 54.
The next digit of our result is 4. 
Result so far: 861.314
Subtract 356 from 410 to get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Going ahead to step 9:
The number 89 fits into 540 6 times, leaving a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 861.3146
The remainder is 6 after subtracting 534 from 540.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 10:
60 divided by 89 is 0 with a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 861.3146
If we take 0 away from 60, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 11:
If we divide 600 by 89, we get 6 and a remainder of 66.
Write down 6 as next digit of the result. 
Result so far: 861.314606
If we take 534 away from 600, we end up with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

On to step 12:
89 goes into 660 7 times with a remainder of 37.
Write down 7 as next digit of the result. 
Result so far: 861.3146067
If we subtract 623 from 660, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Moving on to step 13:
If we divide 370 by 89, we get 4 and a remainder of 14.
Put 4 as the next digit of the answer. 
Result so far: 861.31460674
Subtracting 356 from 370 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

The final result is 861.31460674 with a remainder of 1.4e-08.