2578 ÷ 15 
We want to divide 2578 by 15.

Let's proceed to step 1:
2 divided by 15 is 0 with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 15

Step 2:
15 can be fit into 25 1 times, resulting in a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 15 from 25 and we're left with 10.
Grab the next digit (7) from the dividend, add it to 10, then carry on: 107 / 15

Let's proceed to step 3:
The number 15 fits into 107 7 times, leaving a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 17.0
If we take 105 away from 107, we end up with 2.
Include the next digit (8) from the dividend after 2, then repeat: 28 / 15

Step 4:
If we divide 28 by 15, we get 1 and a remainder of 13.
The next digit of our result is 1. 
Result so far: 171.0
If we take 15 away from 28, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 5:
When dividing 130 by 15, we get 8 with a remainder of 10.
The number 8 becomes the next digit in our result. 
Result so far: 171.8
Subtract 120 from 130 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 6:
100 divided by 15 is 6 with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 171.86
If we take 90 away from 100, 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.

On to step 7:
15 can be fit into 100 6 times, resulting in a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 171.866
Subtracting 90 from 100 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 final result is 171.866 with a remainder of 0.001.