We're dividing 259804 by 19 
We want to figure out the number of times 259804 can be divided by 19.

On to step 1:
The number 19 fits into 2 0 times, leaving a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 19

Going ahead to step 2:
19 can be fit into 25 1 times, resulting in a remainder of 6.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 19 from 25 leaves us with 6.
Include the next digit (9) from the dividend after 6, then repeat: 69 / 19

On to step 3:
If we divide 69 by 19, we get 3 and a remainder of 12.
The next digit of our result is 3. 
Result so far: 13.0
If we take 57 away from 69, we end up with 12.
Include the next digit (8) from the dividend after 12, then repeat: 128 / 19

Step 4:
128 divided by 19 is 6 with a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 136.0
Deduct 114 from 128 and we're left with 14.
Take the next digit (0) from the dividend and append it to 14, then repeat: 140 / 19

Advancing to step 5:
19 goes into 140 7 times with a remainder of 7.
Write down 7 as next digit of the result. 
Result so far: 1367.0
Subtracting 133 from 140 leaves us with 7.
Take the next digit (4) from the dividend and append it to 7, then repeat: 74 / 19

Going ahead to step 6:
19 goes into 74 3 times with a remainder of 17.
Write down 3 as next digit of the result. 
Result so far: 13673.0
Deduct 57 from 74 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 7:
The number 19 fits into 170 8 times, leaving a remainder of 18.
Put 8 as the next digit of the answer. 
Result so far: 13673.8
Deduct 152 from 170 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 8:
When dividing 180 by 19, we get 9 with a remainder of 9.
Write down 9 as next digit of the result. 
Result so far: 13673.89
If we subtract 171 from 180, 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.

Moving on to step 9:
When dividing 90 by 19, we get 4 with a remainder of 14.
The next digit of our result is 4. 
Result so far: 13673.894
Subtracting 76 from 90 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 10:
19 goes into 140 7 times with a remainder of 7.
Put 7 as the next digit of the answer. 
Result so far: 13673.8947
Subtracting 133 from 140 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 11:
The number 19 fits into 70 3 times, leaving a remainder of 13.
Write down 3 as next digit of the result. 
Result so far: 13673.89473
The remainder is 13 after subtracting 57 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 12:
130 divided by 19 is 6 with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 13673.894736
Subtracting 114 from 130 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 13:
If we divide 160 by 19, we get 8 and a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 13673.8947368
Subtracting 152 from 160 leaves us 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.

Let's proceed to step 14:
19 can be fit into 80 4 times, resulting in a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 13673.89473684
The remainder is 4 after subtracting 76 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 13673.89473684, and the remainder is 4e-09.