We're dividing 174261 by 31 
We're looking to find how many times 31 goes into 174261.

Step 1:
31 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 31

Let's proceed to step 2:
31 can be fit into 17 0 times, resulting in a remainder of 17.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 17, we get 17.
Include the next digit (4) from the dividend after 17, then repeat: 174 / 31

On to step 3:
174 divided by 31 is 5 with a remainder of 19.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtract 155 from 174 to get 19.
Include the next digit (2) from the dividend after 19, then repeat: 192 / 31

Let's proceed to step 4:
If we divide 192 by 31, we get 6 and a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 56.0
The remainder is 6 after subtracting 186 from 192.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 31

On to step 5:
When dividing 66 by 31, we get 2 with a remainder of 4.
The next digit of our result is 2. 
Result so far: 562.0
If we take 62 away from 66, we end up with 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 31

Advancing to step 6:
31 can be fit into 41 1 times, resulting in a remainder of 10.
Put 1 as the next digit of the answer. 
Result so far: 5621.0
Subtracting 31 from 41 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 7:
100 divided by 31 is 3 with a remainder of 7.
Use 3 as the next digit of our solution. 
Result so far: 5621.3
The remainder is 7 after subtracting 93 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 8:
70 divided by 31 is 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 5621.32
Subtracting 62 from 70 leaves us 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.

Moving on to step 9:
31 can be fit into 80 2 times, resulting in a remainder of 18.
The next digit of our result is 2. 
Result so far: 5621.322
If we subtract 62 from 80, we 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.

The final result is 5621.322 with a remainder of 0.0018.