175825 ÷ 31 
We're looking to find how many times 31 goes into 175825.

Step 1:
1 divided by 31 is 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 31

Step 2:
31 can be fit into 17 0 times, resulting in a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 17 after subtracting 0 from 17.
Include the next digit (5) from the dividend after 17, then repeat: 175 / 31

Going ahead to step 3:
The number 31 fits into 175 5 times, leaving a remainder of 20.
Put 5 as the next digit of the answer. 
Result so far: 5.0
The remainder is 20 after subtracting 155 from 175.
Include the next digit (8) from the dividend after 20, then repeat: 208 / 31

Moving on to step 4:
When dividing 208 by 31, we get 6 with a remainder of 22.
Write down 6 as next digit of the result. 
Result so far: 56.0
If we take 186 away from 208, we end up with 22.
Append the next digit (2) from the dividend to 22 and continue with: 222 / 31

Moving on to step 5:
222 divided by 31 is 7 with a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 567.0
Deduct 217 from 222 and we're left with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 31

Let's proceed to step 6:
55 divided by 31 is 1 with a remainder of 24.
Record the quotient 1 as the next digit in the result. 
Result so far: 5671.0
If we take 31 away from 55, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 7:
When dividing 240 by 31, we get 7 with a remainder of 23.
Use 7 as the next digit of our solution. 
Result so far: 5671.7
If we take 217 away from 240, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 8:
If we divide 230 by 31, we get 7 and a remainder of 13.
Put 7 as the next digit of the answer. 
Result so far: 5671.77
Subtract 217 from 230 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

In conclusion, the division gives 5671.77 with a balance of 0.013.