114126 divided by 85 
We want to figure out the number of times 114126 can be divided by 85.

Moving on to step 1:
85 goes into 1 0 times with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 85

Moving on to step 2:
The number 85 fits into 11 0 times, leaving a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 11, we get 11.
Include the next digit (4) from the dividend after 11, then repeat: 114 / 85

Advancing to step 3:
If we divide 114 by 85, we get 1 and a remainder of 29.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 85 from 114 leaves us with 29.
Append the next digit (1) from the dividend to 29 and continue with: 291 / 85

Advancing to step 4:
85 can be fit into 291 3 times, resulting in a remainder of 36.
The next digit of our result is 3. 
Result so far: 13.0
Subtract 255 from 291 to get 36.
Append the next digit (2) from the dividend to 36 and continue with: 362 / 85

On to step 5:
85 goes into 362 4 times with a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 134.0
Deduct 340 from 362 and we're left with 22.
Grab the next digit (6) from the dividend, add it to 22, then carry on: 226 / 85

Step 6:
The number 85 fits into 226 2 times, leaving a remainder of 56.
The number 2 becomes the next digit in our result. 
Result so far: 1342.0
Subtract 170 from 226 to get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

On to step 7:
85 can be fit into 560 6 times, resulting in a remainder of 50.
The next digit of our result is 6. 
Result so far: 1342.6
The remainder is 50 after subtracting 510 from 560.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 8:
500 divided by 85 is 5 with a remainder of 75.
Put 5 as the next digit of the answer. 
Result so far: 1342.65
Deduct 425 from 500 and we're left with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

On to step 9:
The number 85 fits into 750 8 times, leaving a remainder of 70.
The next digit of our result is 8. 
Result so far: 1342.658
Subtract 680 from 750 to get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Let's proceed to step 10:
85 can be fit into 700 8 times, resulting in a remainder of 20.
Write down 8 as next digit of the result. 
Result so far: 1342.6588
Subtract 680 from 700 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

After the division, we end up with 1342.6588 and a remainder of 0.0002.