We're dividing 412396 by 31 
We're looking to find how many times 31 goes into 412396.

On to step 1:
The number 31 fits into 4 0 times, leaving a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 31

Moving on to step 2:
If we divide 41 by 31, we get 1 and a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 31 from 41 to get 10.
Grab the next digit (2) from the dividend, add it to 10, then carry on: 102 / 31

On to step 3:
If we divide 102 by 31, we get 3 and a remainder of 9.
The next digit of our result is 3. 
Result so far: 13.0
Deduct 93 from 102 and we're left with 9.
Append the next digit (3) from the dividend to 9 and continue with: 93 / 31

Let's proceed to step 4:
The number 31 fits into 93 3 times, leaving a remainder of 0.
Put 3 as the next digit of the answer. 
Result so far: 133.0
The remainder is 0 after subtracting 93 from 93.
Fetch the next digit (9) from the dividend, attach it to 0 and continue: 9 / 31

Moving on to step 5:
The number 31 fits into 9 0 times, leaving a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 1330.0
Subtract 0 from 9 to get 9.
Bring next digit (6) of the dividend behind the 9 and repeat the process: 96 / 31

Moving on to step 6:
If we divide 96 by 31, we get 3 and a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 13303.0
The remainder is 3 after subtracting 93 from 96.
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:
When dividing 30 by 31, we get 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 13303.0
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.

On to step 8:
When dividing 300 by 31, we get 9 with a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 13303.09
Subtracting 279 from 300 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 9:
31 can be fit into 210 6 times, resulting in a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 13303.096
If we take 186 away from 210, 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.

Advancing to step 10:
The number 31 fits into 240 7 times, leaving a remainder of 23.
The number 7 becomes the next digit in our result. 
Result so far: 13303.0967
Subtracting 217 from 240 leaves us 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.

Let's proceed to step 11:
230 divided by 31 is 7 with a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 13303.09677
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.

Our division results in 13303.09677 with a remaining 1.3e-05.