We look at the division of 213430 by 38 
Our goal is to divide 213430 by 38.

Going ahead to step 1:
When dividing 2 by 38, we get 0 with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 38

On to step 2:
The number 38 fits into 21 0 times, leaving a remainder of 21.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 21 and we're left with 21.
Grab the next digit (3) from the dividend, add it to 21, then carry on: 213 / 38

On to step 3:
When dividing 213 by 38, we get 5 with a remainder of 23.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 190 from 213 leaves us with 23.
Fetch the next digit (4) from the dividend, attach it to 23 and continue: 234 / 38

Moving on to step 4:
234 divided by 38 is 6 with a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 56.0
The remainder is 6 after subtracting 228 from 234.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 38

Moving on to step 5:
38 can be fit into 63 1 times, resulting in a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 561.0
If we take 38 away from 63, we end up with 25.
Bring next digit (0) of the dividend behind the 25 and repeat the process: 250 / 38

Advancing to step 6:
If we divide 250 by 38, we get 6 and a remainder of 22.
Use 6 as the next digit of our solution. 
Result so far: 5616.0
Deduct 228 from 250 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 7:
The number 38 fits into 220 5 times, leaving a remainder of 30.
The number 5 becomes the next digit in our result. 
Result so far: 5616.5
If we subtract 190 from 220, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
300 divided by 38 is 7 with a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 5616.57
If we take 266 away from 300, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 9:
When dividing 340 by 38, we get 8 with a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 5616.578
Deduct 304 from 340 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 10:
The number 38 fits into 360 9 times, leaving a remainder of 18.
The next digit of our result is 9. 
Result so far: 5616.5789
Subtract 342 from 360 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.

Step 11:
If we divide 180 by 38, we get 4 and a remainder of 28.
Record the quotient 4 as the next digit in the result. 
Result so far: 5616.57894
Subtracting 152 from 180 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 12:
280 divided by 38 is 7 with a remainder of 14.
Put 7 as the next digit of the answer. 
Result so far: 5616.578947
Subtract 266 from 280 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 13:
140 divided by 38 is 3 with a remainder of 26.
The next digit of our result is 3. 
Result so far: 5616.5789473
Deduct 114 from 140 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 14:
38 can be fit into 260 6 times, resulting in a remainder of 32.
Put 6 as the next digit of the answer. 
Result so far: 5616.57894736
Subtract 228 from 260 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

After the division, we end up with 5616.57894736 and a remainder of 3.2e-08.