We're dividing 13578 by 27 
We're looking to find how many times 27 goes into 13578.

On to step 1:
1 divided by 27 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 27

Step 2:
27 can be fit into 13 0 times, resulting in a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Grab the next digit (5) from the dividend, add it to 13, then carry on: 135 / 27

On to step 3:
27 can be fit into 135 5 times, resulting in a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we subtract 135 from 135, we get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 27

Step 4:
7 divided by 27 is 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 50.0
Subtract 0 from 7 to get 7.
Append the next digit (8) from the dividend to 7 and continue with: 78 / 27

Going ahead to step 5:
The number 27 fits into 78 2 times, leaving a remainder of 24.
Record the quotient 2 as the next digit in the result. 
Result so far: 502.0
Subtracting 54 from 78 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 6:
When dividing 240 by 27, we get 8 with a remainder of 24.
Use 8 as the next digit of our solution. 
Result so far: 502.8
Subtracting 216 from 240 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 7:
When dividing 240 by 27, we get 8 with a remainder of 24.
Record the quotient 8 as the next digit in the result. 
Result so far: 502.88
If we take 216 away from 240, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The final outcome is 502.88, with a leftover of 0.024.