We're dividing 126113 by 16 
Our goal is to divide 126113 by 16.

Advancing to step 1:
If we divide 1 by 16, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 16

Going ahead to step 2:
The number 16 fits into 12 0 times, leaving a remainder of 12.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 12 after subtracting 0 from 12.
Include the next digit (6) from the dividend after 12, then repeat: 126 / 16

Advancing to step 3:
When dividing 126 by 16, we get 7 with a remainder of 14.
Use 7 as the next digit of our solution. 
Result so far: 7.0
The remainder is 14 after subtracting 112 from 126.
Include the next digit (1) from the dividend after 14, then repeat: 141 / 16

Advancing to step 4:
When dividing 141 by 16, we get 8 with a remainder of 13.
Put 8 as the next digit of the answer. 
Result so far: 78.0
Deduct 128 from 141 and we're left with 13.
Include the next digit (1) from the dividend after 13, then repeat: 131 / 16

Step 5:
The number 16 fits into 131 8 times, leaving a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 788.0
Subtracting 128 from 131 leaves us with 3.
Grab the next digit (3) from the dividend, add it to 3, then carry on: 33 / 16

Let's proceed to step 6:
16 can be fit into 33 2 times, resulting in a remainder of 1.
The next digit of our result is 2. 
Result so far: 7882.0
Subtracting 32 from 33 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.

Going ahead to step 7:
If we divide 10 by 16, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 7882.0
Subtracting 0 from 10 leaves us 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.

Moving on to step 8:
16 goes into 100 6 times with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 7882.06
The remainder is 4 after subtracting 96 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
16 goes into 40 2 times with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 7882.062
Subtract 32 from 40 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 10:
If we divide 80 by 16, we get 5 and a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 7882.0625
If we take 80 away from 80, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 11:
0 divided by 16 is 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 7882.0625
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 12:
16 can be fit into 0 0 times, resulting in a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 7882.0625
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 7882.0625 with a balance of 0.0.