We're dividing 259114 by 16 
We want to figure out the number of times 259114 can be divided by 16.

Let's proceed to step 1:
2 divided by 16 is 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 16

Let's proceed to step 2:
16 goes into 25 1 times with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 16 from 25 leaves us with 9.
Take the next digit (9) from the dividend and append it to 9, then repeat: 99 / 16

Going ahead to step 3:
If we divide 99 by 16, we get 6 and a remainder of 3.
The number 6 becomes the next digit in our result. 
Result so far: 16.0
Subtract 96 from 99 to get 3.
Include the next digit (1) from the dividend after 3, then repeat: 31 / 16

Moving on to step 4:
The number 16 fits into 31 1 times, leaving a remainder of 15.
Record the quotient 1 as the next digit in the result. 
Result so far: 161.0
If we subtract 16 from 31, we get 15.
Grab the next digit (1) from the dividend, add it to 15, then carry on: 151 / 16

Going ahead to step 5:
The number 16 fits into 151 9 times, leaving a remainder of 7.
Record the quotient 9 as the next digit in the result. 
Result so far: 1619.0
The remainder is 7 after subtracting 144 from 151.
Bring next digit (4) of the dividend behind the 7 and repeat the process: 74 / 16

Advancing to step 6:
The number 16 fits into 74 4 times, leaving a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 16194.0
If we take 64 away from 74, we end up 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 7:
100 divided by 16 is 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 16194.6
If we take 96 away from 100, 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.

Advancing to step 8:
16 can be fit into 40 2 times, resulting in a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 16194.62
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.

Advancing to step 9:
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: 16194.625
Subtracting 80 from 80 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 10:
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: 16194.625
Subtract 0 from 0 to 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.

Step 11:
16 goes into 0 0 times with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 16194.625
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.

The final result is 16194.625 with a remainder of 0.0.