We're dividing 259810 by 19 
The aim is to understand the frequency of 19 in 259810.

Step 1:
If we divide 2 by 19, we get 0 and a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 19

Advancing to step 2:
19 goes into 25 1 times with a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 19 from 25, we get 6.
Append the next digit (9) from the dividend to 6 and continue with: 69 / 19

Step 3:
The number 19 fits into 69 3 times, leaving a remainder of 12.
Put 3 as the next digit of the answer. 
Result so far: 13.0
The remainder is 12 after subtracting 57 from 69.
Bring next digit (8) of the dividend behind the 12 and repeat the process: 128 / 19

Moving on to step 4:
128 divided by 19 is 6 with a remainder of 14.
Write down 6 as next digit of the result. 
Result so far: 136.0
The remainder is 14 after subtracting 114 from 128.
Bring next digit (1) of the dividend behind the 14 and repeat the process: 141 / 19

Step 5:
19 can be fit into 141 7 times, resulting in a remainder of 8.
Record the quotient 7 as the next digit in the result. 
Result so far: 1367.0
The remainder is 8 after subtracting 133 from 141.
Take the next digit (0) from the dividend and append it to 8, then repeat: 80 / 19

Going ahead to step 6:
The number 19 fits into 80 4 times, leaving a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 13674.0
If we subtract 76 from 80, 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.

Going ahead to step 7:
19 goes into 40 2 times with a remainder of 2.
Put 2 as the next digit of the answer. 
Result so far: 13674.2
If we subtract 38 from 40, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
If we divide 20 by 19, we get 1 and a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 13674.21
Subtracting 19 from 20 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 9:
If we divide 10 by 19, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 13674.21
Subtracting 0 from 10 leaves us 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.

Advancing to step 10:
19 can be fit into 100 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 13674.2105
The remainder is 5 after subtracting 95 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 11:
50 divided by 19 is 2 with a remainder of 12.
Use 2 as the next digit of our solution. 
Result so far: 13674.21052
If we subtract 38 from 50, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 12:
120 divided by 19 is 6 with a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 13674.210526
Deduct 114 from 120 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 13:
19 can be fit into 60 3 times, resulting in a remainder of 3.
The next digit of our result is 3. 
Result so far: 13674.2105263
Deduct 57 from 60 and we're left 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 14:
30 divided by 19 is 1 with a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 13674.21052631
The remainder is 11 after subtracting 19 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

The final result is 13674.21052631 with a remainder of 1.1e-08.