Let's divide 6259 by 19
Our goal is to divide 6259 by 19.

Going ahead to step 1:
6 divided by 19 is 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (2) from the dividend, attach it to 6 and continue: 62 / 19

Going ahead to step 2:
The number 19 fits into 62 3 times, leaving a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we take 57 away from 62, we end up with 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 19

Advancing to step 3:
The number 19 fits into 55 2 times, leaving a remainder of 17.
Use 2 as the next digit of our solution. 
Result so far: 32.0
Subtract 38 from 55 to get 17.
Include the next digit (9) from the dividend after 17, then repeat: 179 / 19

Advancing to step 4:
19 goes into 179 9 times with a remainder of 8.
Write down 9 as next digit of the result. 
Result so far: 329.0
If we take 171 away from 179, we end up 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.

Moving on to step 5:
If we divide 80 by 19, we get 4 and a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 329.4
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.

On to step 6:
19 goes into 40 2 times with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 329.42
Subtracting 38 from 40 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 7:
19 goes into 20 1 times with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 329.421
If we take 19 away from 20, we end up 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 8:
The number 19 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 329.421
If we take 0 away from 10, 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 9:
When dividing 100 by 19, we get 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 329.42105
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.

On to step 10:
19 goes into 50 2 times with a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 329.421052
Subtracting 38 from 50 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 11:
19 goes into 120 6 times with a remainder of 6.
The next digit of our result is 6. 
Result so far: 329.4210526
Subtract 114 from 120 to get 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 12:
If we divide 60 by 19, we get 3 and a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 329.42105263
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.

In conclusion, the division gives 329.42105263 with a balance of 3e-09.