65577 ÷ 82 
Our goal is to divide 65577 by 82.

Moving on to step 1:
82 goes into 6 0 times with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Grab the next digit (5) from the dividend, add it to 6, then carry on: 65 / 82

Moving on to step 2:
When dividing 65 by 82, we get 0 with a remainder of 65.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 65 to get 65.
Fetch the next digit (5) from the dividend, attach it to 65 and continue: 655 / 82

Moving on to step 3:
When dividing 655 by 82, we get 7 with a remainder of 81.
Put 7 as the next digit of the answer. 
Result so far: 7.0
If we take 574 away from 655, we end up with 81.
Take the next digit (7) from the dividend and append it to 81, then repeat: 817 / 82

Moving on to step 4:
When dividing 817 by 82, we get 9 with a remainder of 79.
Record the quotient 9 as the next digit in the result. 
Result so far: 79.0
If we subtract 738 from 817, we get 79.
Include the next digit (7) from the dividend after 79, then repeat: 797 / 82

Moving on to step 5:
When dividing 797 by 82, we get 9 with a remainder of 59.
The next digit of our result is 9. 
Result so far: 799.0
Deduct 738 from 797 and we're left with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Moving on to step 6:
82 goes into 590 7 times with a remainder of 16.
Use 7 as the next digit of our solution. 
Result so far: 799.7
The remainder is 16 after subtracting 574 from 590.
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 7:
160 divided by 82 is 1 with a remainder of 78.
Use 1 as the next digit of our solution. 
Result so far: 799.71
If we take 82 away from 160, we end up with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Advancing to step 8:
82 can be fit into 780 9 times, resulting in a remainder of 42.
The number 9 becomes the next digit in our result. 
Result so far: 799.719
Subtracting 738 from 780 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 9:
The number 82 fits into 420 5 times, leaving a remainder of 10.
The next digit of our result is 5. 
Result so far: 799.7195
If we subtract 410 from 420, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 10:
The number 82 fits into 100 1 times, leaving a remainder of 18.
The next digit of our result is 1. 
Result so far: 799.71951
If we take 82 away from 100, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 11:
180 divided by 82 is 2 with a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 799.719512
Subtracting 164 from 180 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 12:
If we divide 160 by 82, we get 1 and a remainder of 78.
Write down 1 as next digit of the result. 
Result so far: 799.7195121
Subtracting 82 from 160 leaves us with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

On to step 13:
If we divide 780 by 82, we get 9 and a remainder of 42.
Put 9 as the next digit of the answer. 
Result so far: 799.71951219
The remainder is 42 after subtracting 738 from 780.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

The final outcome is 799.71951219, with a leftover of 4.2e-08.