We look at the division of 172111 by 38 
We're looking to find how many times 38 goes into 172111.

Step 1:
When dividing 1 by 38, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 38

Going ahead to step 2:
When dividing 17 by 38, we get 0 with a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 17 to get 17.
Fetch the next digit (2) from the dividend, attach it to 17 and continue: 172 / 38

Let's proceed to step 3:
When dividing 172 by 38, we get 4 with a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we take 152 away from 172, we end up with 20.
Fetch the next digit (1) from the dividend, attach it to 20 and continue: 201 / 38

On to step 4:
38 goes into 201 5 times with a remainder of 11.
Use 5 as the next digit of our solution. 
Result so far: 45.0
Subtract 190 from 201 to get 11.
Append the next digit (1) from the dividend to 11 and continue with: 111 / 38

On to step 5:
38 can be fit into 111 2 times, resulting in a remainder of 35.
The next digit of our result is 2. 
Result so far: 452.0
Subtracting 76 from 111 leaves us with 35.
Grab the next digit (1) from the dividend, add it to 35, then carry on: 351 / 38

Going ahead to step 6:
38 goes into 351 9 times with a remainder of 9.
The next digit of our result is 9. 
Result so far: 4529.0
If we subtract 342 from 351, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 7:
38 can be fit into 90 2 times, resulting in a remainder of 14.
The next digit of our result is 2. 
Result so far: 4529.2
If we subtract 76 from 90, we 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.

Going ahead to step 8:
38 goes into 140 3 times with a remainder of 26.
Record the quotient 3 as the next digit in the result. 
Result so far: 4529.23
Subtract 114 from 140 to get 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 9:
The number 38 fits into 260 6 times, leaving a remainder of 32.
Put 6 as the next digit of the answer. 
Result so far: 4529.236
Deduct 228 from 260 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 10:
38 goes into 320 8 times with a remainder of 16.
Use 8 as the next digit of our solution. 
Result so far: 4529.2368
The remainder is 16 after subtracting 304 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 11:
The number 38 fits into 160 4 times, leaving a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 4529.23684
If we take 152 away from 160, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 12:
38 goes into 80 2 times with a remainder of 4.
The next digit of our result is 2. 
Result so far: 4529.236842
Subtracting 76 from 80 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 13:
38 goes into 40 1 times with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 4529.2368421
If we subtract 38 from 40, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 14:
If we divide 20 by 38, we get 0 and a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 4529.2368421
If we subtract 0 from 20, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final result is 4529.2368421 with a remainder of 2e-08.