We're dividing 86581 by 13 
Our goal is to divide 86581 by 13.

Moving on to step 1:
The number 13 fits into 8 0 times, leaving a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Fetch the next digit (6) from the dividend, attach it to 8 and continue: 86 / 13

Step 2:
When dividing 86 by 13, we get 6 with a remainder of 8.
The next digit of our result is 6. 
Result so far: 6.0
Subtracting 78 from 86 leaves us with 8.
Append the next digit (5) from the dividend to 8 and continue with: 85 / 13

Moving on to step 3:
The number 13 fits into 85 6 times, leaving a remainder of 7.
Write down 6 as next digit of the result. 
Result so far: 66.0
The remainder is 7 after subtracting 78 from 85.
Take the next digit (8) from the dividend and append it to 7, then repeat: 78 / 13

Step 4:
The number 13 fits into 78 6 times, leaving a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 666.0
Subtracting 78 from 78 leaves us with 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 13

Going ahead to step 5:
The number 13 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 6660.0
If we take 0 away from 1, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 6:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 6660.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 7:
If we divide 100 by 13, we get 7 and a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 6660.07
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 8:
13 goes into 90 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 6660.076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 9:
When dividing 120 by 13, we get 9 with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 6660.0769
Deduct 117 from 120 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 10:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 6660.07692
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 11:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 6660.076923
If we take 39 away from 40, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 12:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 6660.076923
If we subtract 0 from 10, 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 13:
When dividing 100 by 13, we get 7 with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 6660.07692307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Our division results in 6660.07692307 with a remaining 9e-09.