Let's divide 8680 by 13
We want to divide 8680 by 13.

Step 1:
If we divide 8 by 13, we get 0 and a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 8, we end up with 8.
Include the next digit (6) from the dividend after 8, then repeat: 86 / 13

Let's proceed to step 2:
86 divided by 13 is 6 with a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 78 away from 86, we end up with 8.
Take the next digit (8) from the dividend and append it to 8, then repeat: 88 / 13

Going ahead to step 3:
If we divide 88 by 13, we get 6 and a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 66.0
If we take 78 away from 88, we end up with 10.
Append the next digit (0) from the dividend to 10 and continue with: 100 / 13

Going ahead to step 4:
If we divide 100 by 13, we get 7 and a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 667.0
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.

Going ahead to step 5:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 667.6
Deduct 78 from 90 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 6:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 667.69
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 7:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 667.692
Subtract 26 from 30 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 8:
40 divided by 13 is 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 667.6923
Subtracting 39 from 40 leaves us 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.

Let's proceed to step 9:
When dividing 10 by 13, we get 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 667.6923
Subtract 0 from 10 to 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.

Advancing to step 10:
When dividing 100 by 13, we get 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 667.692307
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.

Moving on to step 11:
When dividing 90 by 13, we get 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 667.6923076
If we subtract 78 from 90, we 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.

Advancing to step 12:
13 goes into 120 9 times with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 667.69230769
Subtract 117 from 120 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The final outcome is 667.69230769, with a leftover of 3e-09.