We divide 105031 by 31
We want to figure out the number of times 105031 can be divided by 31.

Step 1:
The number 31 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 31

Moving on to step 2:
If we divide 10 by 31, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Grab the next digit (5) from the dividend, add it to 10, then carry on: 105 / 31

Going ahead to step 3:
31 can be fit into 105 3 times, resulting in a remainder of 12.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
The remainder is 12 after subtracting 93 from 105.
Grab the next digit (0) from the dividend, add it to 12, then carry on: 120 / 31

Advancing to step 4:
31 can be fit into 120 3 times, resulting in a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 33.0
The remainder is 27 after subtracting 93 from 120.
Include the next digit (3) from the dividend after 27, then repeat: 273 / 31

On to step 5:
The number 31 fits into 273 8 times, leaving a remainder of 25.
Use 8 as the next digit of our solution. 
Result so far: 338.0
Subtracting 248 from 273 leaves us with 25.
Fetch the next digit (1) from the dividend, attach it to 25 and continue: 251 / 31

Going ahead to step 6:
The number 31 fits into 251 8 times, leaving a remainder of 3.
The number 8 becomes the next digit in our result. 
Result so far: 3388.0
The remainder is 3 after subtracting 248 from 251.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 7:
If we divide 30 by 31, we get 0 and a remainder of 30.
The number 0 becomes the next digit in our result. 
Result so far: 3388.0
Subtracting 0 from 30 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
When dividing 300 by 31, we get 9 with a remainder of 21.
The next digit of our result is 9. 
Result so far: 3388.09
Subtract 279 from 300 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 9:
The number 31 fits into 210 6 times, leaving a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 3388.096
Subtracting 186 from 210 leaves us 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.

Going ahead to step 10:
31 goes into 240 7 times with a remainder of 23.
Put 7 as the next digit of the answer. 
Result so far: 3388.0967
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 11:
230 divided by 31 is 7 with a remainder of 13.
The next digit of our result is 7. 
Result so far: 3388.09677
If we subtract 217 from 230, we 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.

After the division, we end up with 3388.09677 and a remainder of 1.3e-05.