Let's divide 13564 by 13
We want to figure out the number of times 13564 can be divided by 13.

Advancing to step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 13

Advancing to step 2:
If we divide 13 by 13, we get 1 and a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 13 from 13 to get 0.
Fetch the next digit (5) from the dividend, attach it to 0 and continue: 5 / 13

Advancing to step 3:
When dividing 5 by 13, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 13

On to step 4:
The number 13 fits into 56 4 times, leaving a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 104.0
Subtracting 52 from 56 leaves us with 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 13

Step 5:
If we divide 44 by 13, we get 3 and a remainder of 5.
The next digit of our result is 3. 
Result so far: 1043.0
The remainder is 5 after subtracting 39 from 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 6:
13 can be fit into 50 3 times, resulting in a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 1043.3
Subtract 39 from 50 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 7:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 1043.38
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 8:
13 goes into 60 4 times with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 1043.384
Deduct 52 from 60 and we're left 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.

On to step 9:
13 goes into 80 6 times with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 1043.3846
If we take 78 away from 80, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 10:
When dividing 20 by 13, we get 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 1043.38461
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 11:
13 goes into 70 5 times with a remainder of 5.
The next digit of our result is 5. 
Result so far: 1043.384615
Subtract 65 from 70 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 12:
The number 13 fits into 50 3 times, leaving a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 1043.3846153
If we take 39 away from 50, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 13:
110 divided by 13 is 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 1043.38461538
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final outcome is 1043.38461538, with a leftover of 6e-09.