We divide 136542 by 13
We're looking to find how many times 13 goes into 136542.

Let's proceed to step 1:
The number 13 fits into 1 0 times, leaving 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.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 13

Going ahead to step 2:
13 goes into 13 1 times with a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 13 from 13 and we're left with 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 13

On to step 3:
13 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 10.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (5) from the dividend and append it to 6, then repeat: 65 / 13

Moving on to step 4:
13 goes into 65 5 times with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
The remainder is 0 after subtracting 65 from 65.
Grab the next digit (4) from the dividend, add it to 0, then carry on: 4 / 13

Advancing to step 5:
4 divided by 13 is 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 1050.0
If we subtract 0 from 4, we get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 13

Going ahead to step 6:
When dividing 42 by 13, we get 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 10503.0
If we take 39 away from 42, we end up 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.

Advancing to step 7:
13 can be fit into 30 2 times, resulting in a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 10503.2
Deduct 26 from 30 and we're left 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.

On to step 8:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 10503.23
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.

Let's proceed to step 9:
10 divided by 13 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 10503.23
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.

Advancing to step 10:
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: 10503.2307
If we subtract 91 from 100, we get 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 11:
13 goes into 90 6 times with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 10503.23076
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 12:
If we divide 120 by 13, we get 9 and a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 10503.230769
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.

Step 13:
13 goes into 30 2 times with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 10503.2307692
Deduct 26 from 30 and we're left 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 14:
If we divide 40 by 13, we get 3 and a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 10503.23076923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 10503.23076923 with a balance of 1e-09.