13363 divided by 13 
We're looking to find how many times 13 goes into 13363.

Let's proceed to step 1:
13 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 13

Moving on to step 2:
The number 13 fits into 13 1 times, leaving a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 0 after subtracting 13 from 13.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 13

Going ahead to step 3:
If we divide 3 by 13, we get 0 and a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Subtract 0 from 3 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 13

Advancing to step 4:
If we divide 36 by 13, we get 2 and a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 102.0
Subtracting 26 from 36 leaves us with 10.
Fetch the next digit (3) from the dividend, attach it to 10 and continue: 103 / 13

Let's proceed to step 5:
If we divide 103 by 13, we get 7 and a remainder of 12.
Put 7 as the next digit of the answer. 
Result so far: 1027.0
Subtracting 91 from 103 leaves us 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 6:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 1027.9
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 7:
30 divided by 13 is 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 1027.92
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.

Advancing to step 8:
When dividing 40 by 13, we get 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 1027.923
Subtract 39 from 40 to 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.

Going ahead to step 9:
13 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 1027.923
The remainder is 10 after subtracting 0 from 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 10:
If we divide 100 by 13, we get 7 and a remainder of 9.
The next digit of our result is 7. 
Result so far: 1027.92307
Subtract 91 from 100 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.

Step 11:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 1027.923076
The remainder is 12 after subtracting 78 from 90.
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 12:
When dividing 120 by 13, we get 9 with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 1027.9230769
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 13:
The number 13 fits into 30 2 times, leaving a remainder of 4.
The next digit of our result is 2. 
Result so far: 1027.92307692
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.

In conclusion, the division gives 1027.92307692 with a balance of 4e-09.