We're dividing 546123 by 38 
We're looking to find how many times 38 goes into 546123.

Going ahead to step 1:
If we divide 5 by 38, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 38

Moving on to step 2:
If we divide 54 by 38, we get 1 and a remainder of 16.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 38 from 54 leaves us with 16.
Include the next digit (6) from the dividend after 16, then repeat: 166 / 38

Advancing to step 3:
If we divide 166 by 38, we get 4 and a remainder of 14.
Record the quotient 4 as the next digit in the result. 
Result so far: 14.0
Deduct 152 from 166 and we're left with 14.
Take the next digit (1) from the dividend and append it to 14, then repeat: 141 / 38

On to step 4:
38 goes into 141 3 times with a remainder of 27.
The next digit of our result is 3. 
Result so far: 143.0
If we take 114 away from 141, we end up with 27.
Fetch the next digit (2) from the dividend, attach it to 27 and continue: 272 / 38

Step 5:
272 divided by 38 is 7 with a remainder of 6.
Record the quotient 7 as the next digit in the result. 
Result so far: 1437.0
Deduct 266 from 272 and we're left with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 38

Moving on to step 6:
38 can be fit into 63 1 times, resulting in a remainder of 25.
Record the quotient 1 as the next digit in the result. 
Result so far: 14371.0
The remainder is 25 after subtracting 38 from 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 7:
If we divide 250 by 38, we get 6 and a remainder of 22.
The number 6 becomes the next digit in our result. 
Result so far: 14371.6
Subtract 228 from 250 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.

Going ahead to step 8:
If we divide 220 by 38, we get 5 and a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 14371.65
Subtracting 190 from 220 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 9:
If we divide 300 by 38, we get 7 and a remainder of 34.
Write down 7 as next digit of the result. 
Result so far: 14371.657
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.

Let's proceed to step 10:
If we divide 340 by 38, we get 8 and a remainder of 36.
The number 8 becomes the next digit in our result. 
Result so far: 14371.6578
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.

Moving on to step 11:
When dividing 360 by 38, we get 9 with a remainder of 18.
Put 9 as the next digit of the answer. 
Result so far: 14371.65789
Subtracting 342 from 360 leaves us with 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 12:
If we divide 180 by 38, we get 4 and a remainder of 28.
Put 4 as the next digit of the answer. 
Result so far: 14371.657894
Deduct 152 from 180 and we're left 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.

Step 13:
The number 38 fits into 280 7 times, leaving a remainder of 14.
Use 7 as the next digit of our solution. 
Result so far: 14371.6578947
If we take 266 away from 280, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 14:
38 can be fit into 140 3 times, resulting in a remainder of 26.
The number 3 becomes the next digit in our result. 
Result so far: 14371.65789473
The remainder is 26 after subtracting 114 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

In conclusion, the division gives 14371.65789473 with a balance of 2.6e-08.