We're dividing 8114 by 16 
We're looking to find how many times 16 goes into 8114.

Advancing to step 1:
8 divided by 16 is 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Include the next digit (1) from the dividend after 8, then repeat: 81 / 16

Step 2:
When dividing 81 by 16, we get 5 with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtracting 80 from 81 leaves us with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 16

Let's proceed to step 3:
16 goes into 11 0 times with a remainder of 11.
Write down 0 as next digit of the result. 
Result so far: 50.0
If we subtract 0 from 11, we get 11.
Grab the next digit (4) from the dividend, add it to 11, then carry on: 114 / 16

Step 4:
16 can be fit into 114 7 times, resulting in a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 507.0
Subtracting 112 from 114 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 5:
When dividing 20 by 16, we get 1 with a remainder of 4.
The next digit of our result is 1. 
Result so far: 507.1
If we subtract 16 from 20, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 6:
If we divide 40 by 16, we get 2 and a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 507.12
Deduct 32 from 40 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 7:
16 can be fit into 80 5 times, resulting in a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 507.125
The remainder is 0 after subtracting 80 from 80.
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 8:
When dividing 0 by 16, we get 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 507.125
The remainder is 0 after subtracting 0 from 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 9:
0 divided by 16 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 507.125
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 507.125 and a remainder of 0.0.