We look at the division of 260065 by 19 
Our goal is to divide 260065 by 19.

Let's proceed to step 1:
The number 19 fits into 2 0 times, leaving a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 19

Advancing to step 2:
26 divided by 19 is 1 with a remainder of 7.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 19 from 26 and we're left with 7.
Take the next digit (0) from the dividend and append it to 7, then repeat: 70 / 19

Advancing to step 3:
19 can be fit into 70 3 times, resulting in a remainder of 13.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
The remainder is 13 after subtracting 57 from 70.
Bring next digit (0) of the dividend behind the 13 and repeat the process: 130 / 19

On to step 4:
The number 19 fits into 130 6 times, leaving a remainder of 16.
The next digit of our result is 6. 
Result so far: 136.0
The remainder is 16 after subtracting 114 from 130.
Take the next digit (6) from the dividend and append it to 16, then repeat: 166 / 19

Advancing to step 5:
When dividing 166 by 19, we get 8 with a remainder of 14.
Use 8 as the next digit of our solution. 
Result so far: 1368.0
If we take 152 away from 166, we end up with 14.
Bring next digit (5) of the dividend behind the 14 and repeat the process: 145 / 19

Advancing to step 6:
19 goes into 145 7 times with a remainder of 12.
Use 7 as the next digit of our solution. 
Result so far: 13687.0
Subtract 133 from 145 to 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 7:
The number 19 fits into 120 6 times, leaving a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 13687.6
The remainder is 6 after subtracting 114 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 8:
60 divided by 19 is 3 with a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 13687.63
Subtracting 57 from 60 leaves us 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.

Moving on to step 9:
The number 19 fits into 30 1 times, leaving a remainder of 11.
Write down 1 as next digit of the result. 
Result so far: 13687.631
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.

On to step 10:
19 can be fit into 110 5 times, resulting in a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 13687.6315
If we subtract 95 from 110, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 11:
19 goes into 150 7 times with a remainder of 17.
Record the quotient 7 as the next digit in the result. 
Result so far: 13687.63157
Subtract 133 from 150 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

On to step 12:
If we divide 170 by 19, we get 8 and a remainder of 18.
The number 8 becomes the next digit in our result. 
Result so far: 13687.631578
Subtract 152 from 170 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 13:
If we divide 180 by 19, we get 9 and a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 13687.6315789
Deduct 171 from 180 and we're left with 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 14:
19 goes into 90 4 times with a remainder of 14.
Use 4 as the next digit of our solution. 
Result so far: 13687.63157894
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.

After the division, we end up with 13687.63157894 and a remainder of 1.4e-08.