Let's divide 81931 by 13
Our goal is to divide 81931 by 13.

Advancing to step 1:
The number 13 fits into 8 0 times, leaving a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 13

On to step 2:
If we divide 81 by 13, we get 6 and a remainder of 3.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Deduct 78 from 81 and we're left with 3.
Append the next digit (9) from the dividend to 3 and continue with: 39 / 13

Step 3:
If we divide 39 by 13, we get 3 and a remainder of 0.
The next digit of our result is 3. 
Result so far: 63.0
If we take 39 away from 39, we end up with 0.
Fetch the next digit (3) from the dividend, attach it to 0 and continue: 3 / 13

Step 4:
13 goes into 3 0 times with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 630.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 13

Advancing to step 5:
If we divide 31 by 13, we get 2 and a remainder of 5.
Write down 2 as next digit of the result. 
Result so far: 6302.0
Subtract 26 from 31 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 6:
If we divide 50 by 13, we get 3 and a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 6302.3
Subtract 39 from 50 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 7:
110 divided by 13 is 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 6302.38
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 8:
If we divide 60 by 13, we get 4 and a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 6302.384
If we take 52 away from 60, 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.

Let's proceed to step 9:
13 goes into 80 6 times with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 6302.3846
If we take 78 away from 80, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 10:
20 divided by 13 is 1 with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 6302.38461
If we take 13 away from 20, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 11:
When dividing 70 by 13, we get 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 6302.384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 12:
If we divide 50 by 13, we get 3 and a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 6302.3846153
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 13:
The number 13 fits into 110 8 times, leaving a remainder of 6.
The next digit of our result is 8. 
Result so far: 6302.38461538
Deduct 104 from 110 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 6302.38461538 and a remainder of 6e-09.