We're dividing 82561 by 31 
We want to divide 82561 by 31.

Advancing to step 1:
31 can be fit into 8 0 times, resulting in a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 31

Going ahead to step 2:
31 goes into 82 2 times with a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtract 62 from 82 to get 20.
Include the next digit (5) from the dividend after 20, then repeat: 205 / 31

On to step 3:
The number 31 fits into 205 6 times, leaving a remainder of 19.
The number 6 becomes the next digit in our result. 
Result so far: 26.0
The remainder is 19 after subtracting 186 from 205.
Take the next digit (6) from the dividend and append it to 19, then repeat: 196 / 31

Step 4:
31 goes into 196 6 times with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 266.0
If we take 186 away from 196, we end up with 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 31

Going ahead to step 5:
The number 31 fits into 101 3 times, leaving a remainder of 8.
The number 3 becomes the next digit in our result. 
Result so far: 2663.0
If we take 93 away from 101, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 6:
80 divided by 31 is 2 with a remainder of 18.
Put 2 as the next digit of the answer. 
Result so far: 2663.2
Deduct 62 from 80 and we're left 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.

Moving on to step 7:
The number 31 fits into 180 5 times, leaving a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 2663.25
Subtracting 155 from 180 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 8:
31 goes into 250 8 times with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 2663.258
The remainder is 2 after subtracting 248 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 9:
31 can be fit into 20 0 times, resulting in a remainder of 20.
Record the quotient 0 as the next digit in the result. 
Result so far: 2663.258
Deduct 0 from 20 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 10:
If we divide 200 by 31, we get 6 and a remainder of 14.
Use 6 as the next digit of our solution. 
Result so far: 2663.25806
Subtracting 186 from 200 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.

Going ahead to step 11:
31 goes into 140 4 times with a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 2663.258064
If we subtract 124 from 140, we 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.

Advancing to step 12:
160 divided by 31 is 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 2663.2580645
Subtracting 155 from 160 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 13:
31 goes into 50 1 times with a remainder of 19.
Write down 1 as next digit of the result. 
Result so far: 2663.25806451
Subtract 31 from 50 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

After the division, we end up with 2663.25806451 and a remainder of 1.9e-08.