We look at the division of 114516 by 13 
We want to figure out the number of times 114516 can be divided by 13.

Moving on to step 1:
1 divided by 13 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 13

Going ahead to step 2:
If we divide 11 by 13, we get 0 and a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 11, we get 11.
Append the next digit (4) from the dividend to 11 and continue with: 114 / 13

Let's proceed to step 3:
114 divided by 13 is 8 with a remainder of 10.
The next digit of our result is 8. 
Result so far: 8.0
The remainder is 10 after subtracting 104 from 114.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 13

Step 4:
13 goes into 105 8 times with a remainder of 1.
The next digit of our result is 8. 
Result so far: 88.0
Subtract 104 from 105 to get 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 13

Advancing to step 5:
13 can be fit into 11 0 times, resulting in a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 880.0
If we take 0 away from 11, we end up with 11.
Fetch the next digit (6) from the dividend, attach it to 11 and continue: 116 / 13

Moving on to step 6:
When dividing 116 by 13, we get 8 with a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 8808.0
If we take 104 away from 116, 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.

Advancing 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: 8808.9
Deduct 117 from 120 and we're left 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.

On to step 8:
When dividing 30 by 13, we get 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 8808.92
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.

Let's proceed to step 9:
When dividing 40 by 13, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 8808.923
If we take 39 away from 40, we end up 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 10:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 8808.923
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.

On to step 11:
100 divided by 13 is 7 with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 8808.92307
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.

Let's proceed to step 12:
90 divided by 13 is 6 with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 8808.923076
Deduct 78 from 90 and we're left 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:
13 can be fit into 120 9 times, resulting in a remainder of 3.
The next digit of our result is 9. 
Result so far: 8808.9230769
If we take 117 away from 120, 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.

Step 14:
When dividing 30 by 13, we get 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 8808.92307692
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.

Our division results in 8808.92307692 with a remaining 4e-09.