We're dividing 136665 by 13 
Let's see how many times 13 fits into 136665.

Step 1:
13 can be fit into 1 0 times, resulting in a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 13

Step 2:
The number 13 fits into 13 1 times, leaving a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 13 from 13, we get 0.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 13

Moving on to step 3:
13 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 10.0
Subtracting 0 from 6 leaves us with 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 13

Step 4:
13 can be fit into 66 5 times, resulting in a remainder of 1.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
Subtracting 65 from 66 leaves us with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 13

Advancing to step 5:
The number 13 fits into 16 1 times, leaving a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 1051.0
Subtracting 13 from 16 leaves us with 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 13

On to step 6:
13 can be fit into 35 2 times, resulting in a remainder of 9.
Record the quotient 2 as the next digit in the result. 
Result so far: 10512.0
If we take 26 away from 35, we end up 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.

Let's proceed to step 7:
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: 10512.6
If we take 78 away from 90, we end up 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.

Going ahead to step 8:
120 divided by 13 is 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 10512.69
If we subtract 117 from 120, we 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.

Moving on to step 9:
When dividing 30 by 13, we get 2 with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 10512.692
Subtracting 26 from 30 leaves us with 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 10:
When dividing 40 by 13, we get 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 10512.6923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 11:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 10512.6923
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.

Step 12:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 10512.692307
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.

Going ahead to step 13:
If we divide 90 by 13, we get 6 and a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 10512.6923076
If we take 78 away from 90, we end up 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.

Moving on to step 14:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 10512.69230769
If we subtract 117 from 120, we 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.

Our division results in 10512.69230769 with a remaining 3e-09.