Let's divide 114117 by 26
We're looking to find how many times 26 goes into 114117.

Going ahead to step 1:
If we divide 1 by 26, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 26

Moving on to step 2:
11 divided by 26 is 0 with a remainder of 11.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 11 after subtracting 0 from 11.
Take the next digit (4) from the dividend and append it to 11, then repeat: 114 / 26

Advancing to step 3:
The number 26 fits into 114 4 times, leaving a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtracting 104 from 114 leaves us with 10.
Include the next digit (1) from the dividend after 10, then repeat: 101 / 26

Moving on to step 4:
101 divided by 26 is 3 with a remainder of 23.
Record the quotient 3 as the next digit in the result. 
Result so far: 43.0
The remainder is 23 after subtracting 78 from 101.
Append the next digit (1) from the dividend to 23 and continue with: 231 / 26

On to step 5:
The number 26 fits into 231 8 times, leaving a remainder of 23.
Put 8 as the next digit of the answer. 
Result so far: 438.0
If we subtract 208 from 231, we get 23.
Take the next digit (7) from the dividend and append it to 23, then repeat: 237 / 26

Moving on to step 6:
If we divide 237 by 26, we get 9 and a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 4389.0
Subtracting 234 from 237 leaves us 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.

Let's proceed to step 7:
The number 26 fits into 30 1 times, leaving a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 4389.1
If we take 26 away from 30, we end up 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 8:
If we divide 40 by 26, we get 1 and a remainder of 14.
Put 1 as the next digit of the answer. 
Result so far: 4389.11
The remainder is 14 after subtracting 26 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

The quotient of the division is 4389.11, and the remainder is 0.014.