We look at the division of 510257 by 38 
Our goal is to divide 510257 by 38.

Advancing to step 1:
When dividing 5 by 38, we get 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.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 38

Moving on to step 2:
38 goes into 51 1 times with a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 38 from 51 and we're left with 13.
Bring next digit (0) of the dividend behind the 13 and repeat the process: 130 / 38

On to step 3:
38 goes into 130 3 times with a remainder of 16.
Put 3 as the next digit of the answer. 
Result so far: 13.0
If we take 114 away from 130, we end up with 16.
Append the next digit (2) from the dividend to 16 and continue with: 162 / 38

Step 4:
38 can be fit into 162 4 times, resulting in a remainder of 10.
Put 4 as the next digit of the answer. 
Result so far: 134.0
Deduct 152 from 162 and we're left with 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 38

Moving on to step 5:
If we divide 105 by 38, we get 2 and a remainder of 29.
Write down 2 as next digit of the result. 
Result so far: 1342.0
If we take 76 away from 105, we end up with 29.
Fetch the next digit (7) from the dividend, attach it to 29 and continue: 297 / 38

Step 6:
If we divide 297 by 38, we get 7 and a remainder of 31.
Record the quotient 7 as the next digit in the result. 
Result so far: 13427.0
Subtracting 266 from 297 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 7:
If we divide 310 by 38, we get 8 and a remainder of 6.
The next digit of our result is 8. 
Result so far: 13427.8
If we take 304 away from 310, we end up 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.

Going ahead to step 8:
If we divide 60 by 38, we get 1 and a remainder of 22.
Record the quotient 1 as the next digit in the result. 
Result so far: 13427.81
Subtract 38 from 60 to get 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 9:
The number 38 fits into 220 5 times, leaving a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 13427.815
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.

Step 10:
38 can be fit into 300 7 times, resulting in a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 13427.8157
If we subtract 266 from 300, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 11:
340 divided by 38 is 8 with a remainder of 36.
Put 8 as the next digit of the answer. 
Result so far: 13427.81578
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 12:
When dividing 360 by 38, we get 9 with a remainder of 18.
The next digit of our result is 9. 
Result so far: 13427.815789
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.

Advancing to step 13:
38 goes into 180 4 times with a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 13427.8157894
Subtract 152 from 180 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 14:
When dividing 280 by 38, we get 7 with a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 13427.81578947
The remainder is 14 after subtracting 266 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

The quotient of the division is 13427.81578947, and the remainder is 1.4e-08.