223565 ÷ 13 
We're looking to find how many times 13 goes into 223565.

Going ahead to step 1:
2 divided by 13 is 0 with a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Grab the next digit (2) from the dividend, add it to 2, then carry on: 22 / 13

On to step 2:
If we divide 22 by 13, we get 1 and a remainder of 9.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 13 away from 22, we end up with 9.
Take the next digit (3) from the dividend and append it to 9, then repeat: 93 / 13

Advancing to step 3:
13 can be fit into 93 7 times, resulting in a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 17.0
If we take 91 away from 93, we end up with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 13

Let's proceed to step 4:
If we divide 25 by 13, we get 1 and a remainder of 12.
The number 1 becomes the next digit in our result. 
Result so far: 171.0
Subtracting 13 from 25 leaves us with 12.
Include the next digit (6) from the dividend after 12, then repeat: 126 / 13

Advancing to step 5:
The number 13 fits into 126 9 times, leaving a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 1719.0
The remainder is 9 after subtracting 117 from 126.
Append the next digit (5) from the dividend to 9 and continue with: 95 / 13

Advancing to step 6:
When dividing 95 by 13, we get 7 with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 17197.0
Subtract 91 from 95 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.

Advancing to step 7:
If we divide 40 by 13, we get 3 and a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 17197.3
Subtracting 39 from 40 leaves us 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.

Step 8:
13 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 17197.3
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.

Advancing to step 9:
If we divide 100 by 13, we get 7 and a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 17197.307
Deduct 91 from 100 and we're left with 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 10:
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: 17197.3076
Subtracting 78 from 90 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.

Step 11:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 17197.30769
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.

Going ahead to step 12:
30 divided by 13 is 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 17197.307692
If we take 26 away from 30, we end up 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.

Let's proceed to step 13:
13 goes into 40 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 17197.3076923
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.

Step 14:
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: 17197.3076923
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.

The quotient of the division is 17197.3076923, and the remainder is 1e-08.