We look at the division of 359648 by 31 
We want to figure out the number of times 359648 can be divided by 31.

Advancing to step 1:
When dividing 3 by 31, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Include the next digit (5) from the dividend after 3, then repeat: 35 / 31

Step 2:
The number 31 fits into 35 1 times, leaving a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 31 away from 35, we end up with 4.
Grab the next digit (9) from the dividend, add it to 4, then carry on: 49 / 31

Going ahead to step 3:
The number 31 fits into 49 1 times, leaving a remainder of 18.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
If we take 31 away from 49, we end up with 18.
Bring next digit (6) of the dividend behind the 18 and repeat the process: 186 / 31

On to step 4:
The number 31 fits into 186 6 times, leaving a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 116.0
If we subtract 186 from 186, we get 0.
Take the next digit (4) from the dividend and append it to 0, then repeat: 4 / 31

Moving on to step 5:
31 can be fit into 4 0 times, resulting in a remainder of 4.
The next digit of our result is 0. 
Result so far: 1160.0
If we take 0 away from 4, we end up with 4.
Append the next digit (8) from the dividend to 4 and continue with: 48 / 31

Let's proceed to step 6:
The number 31 fits into 48 1 times, leaving a remainder of 17.
Record the quotient 1 as the next digit in the result. 
Result so far: 11601.0
The remainder is 17 after subtracting 31 from 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 7:
31 can be fit into 170 5 times, resulting in a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 11601.5
If we take 155 away from 170, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
The number 31 fits into 150 4 times, leaving a remainder of 26.
The next digit of our result is 4. 
Result so far: 11601.54
Deduct 124 from 150 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Step 9:
If we divide 260 by 31, we get 8 and a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 11601.548
Deduct 248 from 260 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.

Moving on to step 10:
120 divided by 31 is 3 with a remainder of 27.
The next digit of our result is 3. 
Result so far: 11601.5483
If we subtract 93 from 120, we get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 11:
The number 31 fits into 270 8 times, leaving a remainder of 22.
Record the quotient 8 as the next digit in the result. 
Result so far: 11601.54838
If we take 248 away from 270, we end up 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.

Going ahead to step 12:
31 goes into 220 7 times with a remainder of 3.
The next digit of our result is 7. 
Result so far: 11601.548387
If we subtract 217 from 220, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 13:
31 goes into 30 0 times with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 11601.548387
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 14:
31 goes into 300 9 times with a remainder of 21.
Put 9 as the next digit of the answer. 
Result so far: 11601.54838709
Deduct 279 from 300 and we're left 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.

The final result is 11601.54838709 with a remainder of 2.1e-08.