We look at the division of 542664 by 38 
We're looking to find how many times 38 goes into 542664.

Step 1:
5 divided by 38 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Grab the next digit (4) from the dividend, add it to 5, then carry on: 54 / 38

On to step 2:
38 can be fit into 54 1 times, resulting in a remainder of 16.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 38 from 54 to get 16.
Grab the next digit (2) from the dividend, add it to 16, then carry on: 162 / 38

Moving on to step 3:
The number 38 fits into 162 4 times, leaving a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 14.0
If we take 152 away from 162, we end up with 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 38

Let's proceed to step 4:
38 can be fit into 106 2 times, resulting in a remainder of 30.
The number 2 becomes the next digit in our result. 
Result so far: 142.0
Deduct 76 from 106 and we're left with 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 38

Advancing to step 5:
The number 38 fits into 306 8 times, leaving a remainder of 2.
The next digit of our result is 8. 
Result so far: 1428.0
Subtracting 304 from 306 leaves us with 2.
Include the next digit (4) from the dividend after 2, then repeat: 24 / 38

Advancing to step 6:
If we divide 24 by 38, we get 0 and a remainder of 24.
The next digit of our result is 0. 
Result so far: 14280.0
If we subtract 0 from 24, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 7:
38 can be fit into 240 6 times, resulting in a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 14280.6
The remainder is 12 after subtracting 228 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 8:
When dividing 120 by 38, we get 3 with a remainder of 6.
The next digit of our result is 3. 
Result so far: 14280.63
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.

Let's proceed to step 9:
60 divided by 38 is 1 with a remainder of 22.
Put 1 as the next digit of the answer. 
Result so far: 14280.631
The remainder is 22 after subtracting 38 from 60.
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 10:
38 goes into 220 5 times with a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 14280.6315
The remainder is 30 after subtracting 190 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 11:
When dividing 300 by 38, we get 7 with a remainder of 34.
The next digit of our result is 7. 
Result so far: 14280.63157
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.

Let's proceed to step 12:
If we divide 340 by 38, we get 8 and a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 14280.631578
Subtract 304 from 340 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 13:
The number 38 fits into 360 9 times, leaving a remainder of 18.
The next digit of our result is 9. 
Result so far: 14280.6315789
If we subtract 342 from 360, we 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.

Going ahead to step 14:
The number 38 fits into 180 4 times, leaving a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 14280.63157894
If we take 152 away from 180, we end up 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.

After the division, we end up with 14280.63157894 and a remainder of 2.8e-08.