309360 ÷ 13 
We want to figure out the number of times 309360 can be divided by 13.

Going ahead to step 1:
3 divided by 13 is 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Take the next digit (0) from the dividend and append it to 3, then repeat: 30 / 13

On to step 2:
When dividing 30 by 13, we get 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
The remainder is 4 after subtracting 26 from 30.
Include the next digit (9) from the dividend after 4, then repeat: 49 / 13

Advancing to step 3:
13 goes into 49 3 times with a remainder of 10.
The next digit of our result is 3. 
Result so far: 23.0
Subtracting 39 from 49 leaves us with 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 13

On to step 4:
103 divided by 13 is 7 with a remainder of 12.
The number 7 becomes the next digit in our result. 
Result so far: 237.0
The remainder is 12 after subtracting 91 from 103.
Bring next digit (6) of the dividend behind the 12 and repeat the process: 126 / 13

Let's proceed to step 5:
13 can be fit into 126 9 times, resulting in a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 2379.0
If we take 117 away from 126, we end up with 9.
Grab the next digit (0) from the dividend, add it to 9, then carry on: 90 / 13

Let's proceed to step 6:
When dividing 90 by 13, we get 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 23796.0
If we subtract 78 from 90, 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.

Advancing to step 7:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 23796.9
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.

Moving on to step 8:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 23796.92
Subtract 26 from 30 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 9:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 23796.923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 10:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 23796.923
If we take 0 away from 10, we end up 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.

Step 11:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 23796.92307
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.

Moving on to step 12:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 23796.923076
If we subtract 78 from 90, 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 13:
13 can be fit into 120 9 times, resulting in a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 23796.9230769
Subtracting 117 from 120 leaves us 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 14:
If we divide 30 by 13, we get 2 and a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 23796.92307692
Subtract 26 from 30 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final result is 23796.92307692 with a remainder of 4e-09.