We're dividing 131364 by 13 
We're looking to find how many times 13 goes into 131364.

Step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 13

Step 2:
If we divide 13 by 13, we get 1 and a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 13 from 13 and we're left with 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 13

Step 3:
1 divided by 13 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 13

Moving on to step 4:
The number 13 fits into 13 1 times, leaving a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 101.0
If we take 13 away from 13, we end up with 0.
Include the next digit (6) from the dividend after 0, then repeat: 6 / 13

Moving on to step 5:
13 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 1010.0
If we take 0 away from 6, we end up with 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 13

On to step 6:
13 can be fit into 64 4 times, resulting in a remainder of 12.
The next digit of our result is 4. 
Result so far: 10104.0
If we take 52 away from 64, 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 7:
The number 13 fits into 120 9 times, leaving a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 10104.9
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.

On to step 8:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 10104.92
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.

Let's proceed to step 9:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 10104.923
Deduct 39 from 40 and we're left 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.

Step 10:
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: 10104.923
If we take 0 away from 10, we end up 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.

Going ahead to step 11:
When dividing 100 by 13, we get 7 with a remainder of 9.
The next digit of our result is 7. 
Result so far: 10104.92307
Subtracting 91 from 100 leaves us 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.

Step 12:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 10104.923076
Subtracting 78 from 90 leaves us 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 13:
120 divided by 13 is 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 10104.9230769
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.

Step 14:
30 divided by 13 is 2 with a remainder of 4.
The next digit of our result is 2. 
Result so far: 10104.92307692
If we subtract 26 from 30, we 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.

In conclusion, the division gives 10104.92307692 with a balance of 4e-09.