We're dividing 8578071 by 678 
We're looking to find how many times 678 goes into 8578071.

Step 1:
When dividing 8 by 678, we get 0 with a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Fetch the next digit (5) from the dividend, attach it to 8 and continue: 85 / 678

Step 2:
When dividing 85 by 678, we get 0 with a remainder of 85.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 85 after subtracting 0 from 85.
Grab the next digit (7) from the dividend, add it to 85, then carry on: 857 / 678

Let's proceed to step 3:
When dividing 857 by 678, we get 1 with a remainder of 179.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 678 from 857 leaves us with 179.
Take the next digit (8) from the dividend and append it to 179, then repeat: 1798 / 678

Step 4:
If we divide 1798 by 678, we get 2 and a remainder of 442.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Deduct 1356 from 1798 and we're left with 442.
Grab the next digit (0) from the dividend, add it to 442, then carry on: 4420 / 678

Let's proceed to step 5:
If we divide 4420 by 678, we get 6 and a remainder of 352.
The next digit of our result is 6. 
Result so far: 126.0
Subtract 4068 from 4420 to get 352.
Take the next digit (7) from the dividend and append it to 352, then repeat: 3527 / 678

Going ahead to step 6:
The number 678 fits into 3527 5 times, leaving a remainder of 137.
The number 5 becomes the next digit in our result. 
Result so far: 1265.0
Subtracting 3390 from 3527 leaves us with 137.
Grab the next digit (1) from the dividend, add it to 137, then carry on: 1371 / 678

Moving on to step 7:
678 goes into 1371 2 times with a remainder of 15.
Put 2 as the next digit of the answer. 
Result so far: 12652.0
Subtracting 1356 from 1371 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
678 goes into 150 0 times with a remainder of 150.
Put 0 as the next digit of the answer. 
Result so far: 12652.0
Subtracting 0 from 150 leaves us with 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1500, and continue the process.

Going ahead to step 9:
678 goes into 1500 2 times with a remainder of 144.
Record the quotient 2 as the next digit in the result. 
Result so far: 12652.02
If we take 1356 away from 1500, we end up with 144.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1440, and continue the process.

Advancing to step 10:
When dividing 1440 by 678, we get 2 with a remainder of 84.
Write down 2 as next digit of the result. 
Result so far: 12652.022
Deduct 1356 from 1440 and we're left with 84.
Since there are no more digits in the dividend, we add a zero to the remainder making it 840, and continue the process.

The final result is 12652.022 with a remainder of 0.0084.