We look at the division of 263417 by 19 
Our goal is to divide 263417 by 19.

Advancing to step 1:
When dividing 2 by 19, we get 0 with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Append the next digit (6) from the dividend to 2 and continue with: 26 / 19

On to step 2:
26 divided by 19 is 1 with a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 19 from 26 to get 7.
Include the next digit (3) from the dividend after 7, then repeat: 73 / 19

Advancing to step 3:
73 divided by 19 is 3 with a remainder of 16.
The next digit of our result is 3. 
Result so far: 13.0
The remainder is 16 after subtracting 57 from 73.
Append the next digit (4) from the dividend to 16 and continue with: 164 / 19

Step 4:
19 can be fit into 164 8 times, resulting in a remainder of 12.
The next digit of our result is 8. 
Result so far: 138.0
Deduct 152 from 164 and we're left with 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 19

Step 5:
121 divided by 19 is 6 with a remainder of 7.
The next digit of our result is 6. 
Result so far: 1386.0
If we take 114 away from 121, we end up with 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 19

Going ahead to step 6:
19 can be fit into 77 4 times, resulting in a remainder of 1.
The next digit of our result is 4. 
Result so far: 13864.0
Subtracting 76 from 77 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.

Moving on to step 7:
If we divide 10 by 19, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 13864.0
Subtract 0 from 10 to get 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 8:
When dividing 100 by 19, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 13864.05
Subtract 95 from 100 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 9:
50 divided by 19 is 2 with a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 13864.052
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.

On to step 10:
120 divided by 19 is 6 with a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 13864.0526
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 11:
19 can be fit into 60 3 times, resulting in a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 13864.05263
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.

Going ahead to step 12:
When dividing 30 by 19, we get 1 with a remainder of 11.
Write down 1 as next digit of the result. 
Result so far: 13864.052631
Subtract 19 from 30 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 13:
110 divided by 19 is 5 with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 13864.0526315
Subtracting 95 from 110 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 14:
19 goes into 150 7 times with a remainder of 17.
Use 7 as the next digit of our solution. 
Result so far: 13864.05263157
The remainder is 17 after subtracting 133 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Our division results in 13864.05263157 with a remaining 1.7e-08.