We look at the division of 124325 by 19 
We want to divide 124325 by 19.

Advancing to step 1:
19 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 19

Step 2:
If we divide 12 by 19, we get 0 and a remainder of 12.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 12 after subtracting 0 from 12.
Fetch the next digit (4) from the dividend, attach it to 12 and continue: 124 / 19

Step 3:
When dividing 124 by 19, we get 6 with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Deduct 114 from 124 and we're left with 10.
Grab the next digit (3) from the dividend, add it to 10, then carry on: 103 / 19

Step 4:
When dividing 103 by 19, we get 5 with a remainder of 8.
Write down 5 as next digit of the result. 
Result so far: 65.0
Deduct 95 from 103 and we're left with 8.
Include the next digit (2) from the dividend after 8, then repeat: 82 / 19

On to step 5:
If we divide 82 by 19, we get 4 and a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 654.0
The remainder is 6 after subtracting 76 from 82.
Include the next digit (5) from the dividend after 6, then repeat: 65 / 19

Going ahead to step 6:
When dividing 65 by 19, we get 3 with a remainder of 8.
Put 3 as the next digit of the answer. 
Result so far: 6543.0
If we subtract 57 from 65, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 7:
The number 19 fits into 80 4 times, leaving a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 6543.4
If we take 76 away from 80, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
19 goes into 40 2 times with a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 6543.42
Deduct 38 from 40 and we're left 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.

Let's proceed to step 9:
The number 19 fits into 20 1 times, leaving a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 6543.421
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.

Step 10:
19 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 6543.421
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.

Advancing to step 11:
If we divide 100 by 19, we get 5 and a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 6543.42105
Deduct 95 from 100 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 12:
50 divided by 19 is 2 with a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 6543.421052
If we take 38 away from 50, we end up 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.

Moving on to step 13:
19 goes into 120 6 times with a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 6543.4210526
Subtracting 114 from 120 leaves us 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.

Moving on to step 14:
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: 6543.42105263
If we take 57 away from 60, we end up 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 6543.42105263 with a balance of 3e-09.