10117 divided by 31 
We want to figure out the number of times 10117 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.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 31

On to step 2:
When dividing 10 by 31, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Include the next digit (1) from the dividend after 10, then repeat: 101 / 31

Step 3:
31 can be fit into 101 3 times, resulting in a remainder of 8.
Put 3 as the next digit of the answer. 
Result so far: 3.0
Subtracting 93 from 101 leaves us with 8.
Include the next digit (1) from the dividend after 8, then repeat: 81 / 31

Going ahead to step 4:
31 can be fit into 81 2 times, resulting in a remainder of 19.
The number 2 becomes the next digit in our result. 
Result so far: 32.0
Deduct 62 from 81 and we're left with 19.
Grab the next digit (7) from the dividend, add it to 19, then carry on: 197 / 31

Step 5:
The number 31 fits into 197 6 times, leaving a remainder of 11.
Use 6 as the next digit of our solution. 
Result so far: 326.0
If we subtract 186 from 197, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 6:
31 goes into 110 3 times with a remainder of 17.
The number 3 becomes the next digit in our result. 
Result so far: 326.3
Subtract 93 from 110 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 7:
The number 31 fits into 170 5 times, leaving a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 326.35
Subtracting 155 from 170 leaves us 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.

Going ahead to step 8:
31 can be fit into 150 4 times, resulting in a remainder of 26.
The number 4 becomes the next digit in our result. 
Result so far: 326.354
If we take 124 away from 150, we end up 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.

Moving on to step 9:
31 can be fit into 260 8 times, resulting in a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 326.3548
If we subtract 248 from 260, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 10:
31 goes into 120 3 times with a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 326.35483
Deduct 93 from 120 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 11:
31 can be fit into 270 8 times, resulting in a remainder of 22.
Record the quotient 8 as the next digit in the result. 
Result so far: 326.354838
Subtracting 248 from 270 leaves us 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.

Let's proceed to step 12:
The number 31 fits into 220 7 times, leaving a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 326.3548387
Subtract 217 from 220 to 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 can be fit into 30 0 times, resulting in a remainder of 30.
The next digit of our result is 0. 
Result so far: 326.3548387
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.

In conclusion, the division gives 326.3548387 with a balance of 3e-08.