We're dividing 108597 by 31 
We want to figure out the number of times 108597 can be divided by 31.

On to 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
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 31

Step 2:
If we divide 10 by 31, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Take the next digit (8) from the dividend and append it to 10, then repeat: 108 / 31

On to step 3:
If we divide 108 by 31, we get 3 and a remainder of 15.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 15 after subtracting 93 from 108.
Fetch the next digit (5) from the dividend, attach it to 15 and continue: 155 / 31

On to step 4:
31 can be fit into 155 5 times, resulting in a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 35.0
Deduct 155 from 155 and we're left with 0.
Grab the next digit (9) from the dividend, add it to 0, then carry on: 9 / 31

On to step 5:
When dividing 9 by 31, we get 0 with a remainder of 9.
Use 0 as the next digit of our solution. 
Result so far: 350.0
Subtracting 0 from 9 leaves us with 9.
Include the next digit (7) from the dividend after 9, then repeat: 97 / 31

On to step 6:
31 goes into 97 3 times with a remainder of 4.
The number 3 becomes the next digit in our result. 
Result so far: 3503.0
Deduct 93 from 97 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
The number 31 fits into 40 1 times, leaving a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 3503.1
Subtract 31 from 40 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 8:
31 goes into 90 2 times with a remainder of 28.
Record the quotient 2 as the next digit in the result. 
Result so far: 3503.12
If we subtract 62 from 90, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 9:
31 can be fit into 280 9 times, resulting in a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 3503.129
If we subtract 279 from 280, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 10:
The number 31 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 3503.129
Subtracting 0 from 10 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.

Let's proceed to step 11:
31 can be fit into 100 3 times, resulting in a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 3503.12903
Subtracting 93 from 100 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 12:
31 goes into 70 2 times with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 3503.129032
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.

Advancing to step 13:
31 can be fit into 80 2 times, resulting in a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 3503.1290322
Subtracting 62 from 80 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

In conclusion, the division gives 3503.1290322 with a balance of 1.8e-07.