We look at the division of 43174 by 38 
We're looking to find how many times 38 goes into 43174.

Advancing to step 1:
The number 38 fits into 4 0 times, leaving a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 38

Step 2:
43 divided by 38 is 1 with a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 38 from 43 to get 5.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 38

Going ahead to step 3:
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: 11.0
If we subtract 38 from 51, we get 13.
Append the next digit (7) from the dividend to 13 and continue with: 137 / 38

Going ahead to step 4:
When dividing 137 by 38, we get 3 with a remainder of 23.
The next digit of our result is 3. 
Result so far: 113.0
If we subtract 114 from 137, we get 23.
Include the next digit (4) from the dividend after 23, then repeat: 234 / 38

Moving on to step 5:
38 goes into 234 6 times with a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 1136.0
Subtracting 228 from 234 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.

Advancing to step 6:
The number 38 fits into 60 1 times, leaving a remainder of 22.
The next digit of our result is 1. 
Result so far: 1136.1
If we take 38 away from 60, we end up 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:
38 goes into 220 5 times with a remainder of 30.
The next digit of our result is 5. 
Result so far: 1136.15
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.

Moving on to step 8:
If we divide 300 by 38, we get 7 and a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 1136.157
Subtracting 266 from 300 leaves us 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 9:
340 divided by 38 is 8 with a remainder of 36.
Put 8 as the next digit of the answer. 
Result so far: 1136.1578
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.

Let's proceed to step 10:
If we divide 360 by 38, we get 9 and a remainder of 18.
Record the quotient 9 as the next digit in the result. 
Result so far: 1136.15789
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.

Let's proceed to step 11:
180 divided by 38 is 4 with a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 1136.157894
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:
The number 38 fits into 280 7 times, leaving a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 1136.1578947
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.

Advancing to step 13:
If we divide 140 by 38, we get 3 and a remainder of 26.
The number 3 becomes the next digit in our result. 
Result so far: 1136.15789473
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.

Our division results in 1136.15789473 with a remaining 2.6e-08.