665583 ÷ 78 
We're looking to find how many times 78 goes into 665583.

Advancing to step 1:
The number 78 fits into 6 0 times, leaving a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Append the next digit (6) from the dividend to 6 and continue with: 66 / 78

Step 2:
The number 78 fits into 66 0 times, leaving a remainder of 66.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 66, we end up with 66.
Include the next digit (5) from the dividend after 66, then repeat: 665 / 78

Moving on to step 3:
78 can be fit into 665 8 times, resulting in a remainder of 41.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we subtract 624 from 665, we get 41.
Take the next digit (5) from the dividend and append it to 41, then repeat: 415 / 78

Advancing to step 4:
78 goes into 415 5 times with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 85.0
The remainder is 25 after subtracting 390 from 415.
Grab the next digit (8) from the dividend, add it to 25, then carry on: 258 / 78

Moving on to step 5:
The number 78 fits into 258 3 times, leaving a remainder of 24.
The number 3 becomes the next digit in our result. 
Result so far: 853.0
If we take 234 away from 258, we end up with 24.
Include the next digit (3) from the dividend after 24, then repeat: 243 / 78

On to step 6:
The number 78 fits into 243 3 times, leaving a remainder of 9.
Use 3 as the next digit of our solution. 
Result so far: 8533.0
Subtract 234 from 243 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 7:
78 can be fit into 90 1 times, resulting in a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 8533.1
Deduct 78 from 90 and we're left 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.

Moving on to step 8:
78 goes into 120 1 times with a remainder of 42.
The number 1 becomes the next digit in our result. 
Result so far: 8533.11
Subtracting 78 from 120 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Our division results in 8533.11 with a remaining 0.042.