We're dividing 126538 by 11 
We're looking to find how many times 11 goes into 126538.

Step 1:
11 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 11

Going ahead to step 2:
If we divide 12 by 11, we get 1 and a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 11 away from 12, we end up with 1.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 11

Step 3:
11 can be fit into 16 1 times, resulting in a remainder of 5.
The next digit of our result is 1. 
Result so far: 11.0
If we subtract 11 from 16, we get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 11

Going ahead to step 4:
11 goes into 55 5 times with a remainder of 0.
The next digit of our result is 5. 
Result so far: 115.0
Subtract 55 from 55 to get 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 11

Going ahead to step 5:
3 divided by 11 is 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 1150.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (8) from the dividend to 3 and continue with: 38 / 11

Let's proceed to step 6:
When dividing 38 by 11, we get 3 with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 11503.0
Subtracting 33 from 38 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 7:
11 can be fit into 50 4 times, resulting in a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 11503.4
If we subtract 44 from 50, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 8:
When dividing 60 by 11, we get 5 with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 11503.45
Subtract 55 from 60 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 9:
50 divided by 11 is 4 with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 11503.454
Subtract 44 from 50 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 10:
If we divide 60 by 11, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 11503.4545
Subtract 55 from 60 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 11:
When dividing 50 by 11, we get 4 with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 11503.45454
Deduct 44 from 50 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 12:
The number 11 fits into 60 5 times, leaving a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 11503.454545
Subtract 55 from 60 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 13:
50 divided by 11 is 4 with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 11503.4545454
Subtracting 44 from 50 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 14:
When dividing 60 by 11, we get 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 11503.45454545
Deduct 55 from 60 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final outcome is 11503.45454545, with a leftover of 5e-09.