Let's divide 21338 by 19
We want to divide 21338 by 19.

Going ahead to step 1:
When dividing 2 by 19, we get 0 with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Take the next digit (1) from the dividend and append it to 2, then repeat: 21 / 19

Going ahead to step 2:
19 goes into 21 1 times with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 19 from 21 leaves us with 2.
Include the next digit (3) from the dividend after 2, then repeat: 23 / 19

On to step 3:
23 divided by 19 is 1 with a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
The remainder is 4 after subtracting 19 from 23.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 19

Advancing to step 4:
When dividing 43 by 19, we get 2 with a remainder of 5.
Record the quotient 2 as the next digit in the result. 
Result so far: 112.0
The remainder is 5 after subtracting 38 from 43.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 19

Moving on to step 5:
The number 19 fits into 58 3 times, leaving a remainder of 1.
The next digit of our result is 3. 
Result so far: 1123.0
Subtract 57 from 58 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 6:
19 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 1123.0
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.

On to step 7:
The number 19 fits into 100 5 times, leaving a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 1123.05
If we take 95 away from 100, we end up 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.

On to step 8:
50 divided by 19 is 2 with a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 1123.052
The remainder is 12 after subtracting 38 from 50.
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 9:
120 divided by 19 is 6 with a remainder of 6.
The next digit of our result is 6. 
Result so far: 1123.0526
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.

On to step 10:
The number 19 fits into 60 3 times, leaving a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 1123.05263
The remainder is 3 after subtracting 57 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 11:
30 divided by 19 is 1 with a remainder of 11.
The next digit of our result is 1. 
Result so far: 1123.052631
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.

Moving on to step 12:
110 divided by 19 is 5 with a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 1123.0526315
The remainder is 15 after subtracting 95 from 110.
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 13:
The number 19 fits into 150 7 times, leaving a remainder of 17.
Use 7 as the next digit of our solution. 
Result so far: 1123.05263157
Deduct 133 from 150 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

The final outcome is 1123.05263157, with a leftover of 1.7e-08.