678413 divided by 75 
Let's see how many times 75 fits into 678413.

Moving on to step 1:
75 goes into 6 0 times with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 75

Moving on to step 2:
67 divided by 75 is 0 with a remainder of 67.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 67, we get 67.
Include the next digit (8) from the dividend after 67, then repeat: 678 / 75

Moving on to step 3:
The number 75 fits into 678 9 times, leaving a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
Subtract 675 from 678 to get 3.
Fetch the next digit (4) from the dividend, attach it to 3 and continue: 34 / 75

On to step 4:
75 goes into 34 0 times with a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 90.0
Subtract 0 from 34 to get 34.
Grab the next digit (1) from the dividend, add it to 34, then carry on: 341 / 75

Moving on to step 5:
341 divided by 75 is 4 with a remainder of 41.
Write down 4 as next digit of the result. 
Result so far: 904.0
If we take 300 away from 341, we end up with 41.
Grab the next digit (3) from the dividend, add it to 41, then carry on: 413 / 75

Going ahead to step 6:
75 can be fit into 413 5 times, resulting in a remainder of 38.
Record the quotient 5 as the next digit in the result. 
Result so far: 9045.0
If we subtract 375 from 413, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 7:
75 can be fit into 380 5 times, resulting in a remainder of 5.
The next digit of our result is 5. 
Result so far: 9045.5
If we subtract 375 from 380, we 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.

On to step 8:
If we divide 50 by 75, we get 0 and a remainder of 50.
The next digit of our result is 0. 
Result so far: 9045.5
The remainder is 50 after subtracting 0 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 9:
500 divided by 75 is 6 with a remainder of 50.
Record the quotient 6 as the next digit in the result. 
Result so far: 9045.506
If we subtract 450 from 500, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 10:
75 can be fit into 500 6 times, resulting in a remainder of 50.
Put 6 as the next digit of the answer. 
Result so far: 9045.5066
If we subtract 450 from 500, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final result is 9045.5066 with a remainder of 0.0005.