172525 ÷ 38 
Our goal is to divide 172525 by 38.

Let's proceed to step 1:
If we divide 1 by 38, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 38

Advancing to step 2:
38 goes into 17 0 times with a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Bring next digit (2) of the dividend behind the 17 and repeat the process: 172 / 38

On to step 3:
172 divided by 38 is 4 with a remainder of 20.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Deduct 152 from 172 and we're left with 20.
Fetch the next digit (5) from the dividend, attach it to 20 and continue: 205 / 38

Moving on to step 4:
205 divided by 38 is 5 with a remainder of 15.
The next digit of our result is 5. 
Result so far: 45.0
Deduct 190 from 205 and we're left with 15.
Include the next digit (2) from the dividend after 15, then repeat: 152 / 38

Moving on to step 5:
If we divide 152 by 38, we get 4 and a remainder of 0.
Use 4 as the next digit of our solution. 
Result so far: 454.0
If we take 152 away from 152, we end up with 0.
Fetch the next digit (5) from the dividend, attach it to 0 and continue: 5 / 38

Advancing to step 6:
38 goes into 5 0 times with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 4540.0
The remainder is 5 after subtracting 0 from 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 7:
38 can be fit into 50 1 times, resulting in a remainder of 12.
Use 1 as the next digit of our solution. 
Result so far: 4540.1
Deduct 38 from 50 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 8:
38 can be fit into 120 3 times, resulting in a remainder of 6.
Use 3 as the next digit of our solution. 
Result so far: 4540.13
If we take 114 away from 120, 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.

Let's proceed to step 9:
60 divided by 38 is 1 with a remainder of 22.
The next digit of our result is 1. 
Result so far: 4540.131
Deduct 38 from 60 and we're left 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.

Let's proceed to step 10:
When dividing 220 by 38, we get 5 with a remainder of 30.
The next digit of our result is 5. 
Result so far: 4540.1315
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:
300 divided by 38 is 7 with a remainder of 34.
Use 7 as the next digit of our solution. 
Result so far: 4540.13157
Deduct 266 from 300 and we're left 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:
The number 38 fits into 340 8 times, leaving a remainder of 36.
Use 8 as the next digit of our solution. 
Result so far: 4540.131578
Subtracting 304 from 340 leaves us 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.

Let's proceed to step 13:
When dividing 360 by 38, we get 9 with a remainder of 18.
The next digit of our result is 9. 
Result so far: 4540.1315789
If we take 342 away from 360, we end up 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.

Step 14:
The number 38 fits into 180 4 times, leaving a remainder of 28.
Put 4 as the next digit of the answer. 
Result so far: 4540.13157894
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.

After the division, we end up with 4540.13157894 and a remainder of 2.8e-08.