We divide 309117 by 13
We want to figure out the number of times 309117 can be divided by 13.

Advancing to step 1:
When dividing 3 by 13, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 13

Advancing to step 2:
If we divide 30 by 13, we get 2 and a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 2.0
Subtracting 26 from 30 leaves us with 4.
Append the next digit (9) from the dividend to 4 and continue with: 49 / 13

Let's proceed to step 3:
The number 13 fits into 49 3 times, leaving a remainder of 10.
Record the quotient 3 as the next digit in the result. 
Result so far: 23.0
Deduct 39 from 49 and we're left with 10.
Grab the next digit (1) from the dividend, add it to 10, then carry on: 101 / 13

Let's proceed to step 4:
13 can be fit into 101 7 times, resulting in a remainder of 10.
The number 7 becomes the next digit in our result. 
Result so far: 237.0
Deduct 91 from 101 and we're left with 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 13

Step 5:
13 goes into 101 7 times with a remainder of 10.
The next digit of our result is 7. 
Result so far: 2377.0
If we take 91 away from 101, we end up with 10.
Append the next digit (7) from the dividend to 10 and continue with: 107 / 13

Going ahead to step 6:
13 goes into 107 8 times with a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 23778.0
If we subtract 104 from 107, 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.

Moving on to step 7:
When dividing 30 by 13, we get 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 23778.2
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
13 goes into 40 3 times with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 23778.23
If we take 39 away from 40, we end up with 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 9:
10 divided by 13 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 23778.23
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 10:
100 divided by 13 is 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 23778.2307
If we subtract 91 from 100, we 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.

Let's proceed to step 11:
13 goes into 90 6 times with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 23778.23076
If we take 78 away from 90, we end up 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.

Step 12:
13 goes into 120 9 times with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 23778.230769
Deduct 117 from 120 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 13:
When dividing 30 by 13, we get 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 23778.2307692
Deduct 26 from 30 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.

Step 14:
If we divide 40 by 13, we get 3 and a remainder of 1.
The next digit of our result is 3. 
Result so far: 23778.23076923
Deduct 39 from 40 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 23778.23076923 with a balance of 1e-09.