510614 divided by 75 
Let's see how many times 75 fits into 510614.

Moving on to step 1:
When dividing 5 by 75, we get 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 75

Going ahead to step 2:
If we divide 51 by 75, we get 0 and a remainder of 51.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 51 leaves us with 51.
Grab the next digit (0) from the dividend, add it to 51, then carry on: 510 / 75

On to step 3:
The number 75 fits into 510 6 times, leaving a remainder of 60.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 450 from 510, we get 60.
Bring next digit (6) of the dividend behind the 60 and repeat the process: 606 / 75

Advancing to step 4:
The number 75 fits into 606 8 times, leaving a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 68.0
The remainder is 6 after subtracting 600 from 606.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 75

Let's proceed to step 5:
When dividing 61 by 75, we get 0 with a remainder of 61.
The number 0 becomes the next digit in our result. 
Result so far: 680.0
If we take 0 away from 61, we end up with 61.
Grab the next digit (4) from the dividend, add it to 61, then carry on: 614 / 75

Moving on to step 6:
75 goes into 614 8 times with a remainder of 14.
The next digit of our result is 8. 
Result so far: 6808.0
If we take 600 away from 614, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 7:
If we divide 140 by 75, we get 1 and a remainder of 65.
Record the quotient 1 as the next digit in the result. 
Result so far: 6808.1
Subtract 75 from 140 to get 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Step 8:
If we divide 650 by 75, we get 8 and a remainder of 50.
The number 8 becomes the next digit in our result. 
Result so far: 6808.18
If we subtract 600 from 650, 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.

Step 9:
75 goes into 500 6 times with a remainder of 50.
Record the quotient 6 as the next digit in the result. 
Result so far: 6808.186
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.

Advancing to step 10:
500 divided by 75 is 6 with a remainder of 50.
The number 6 becomes the next digit in our result. 
Result so far: 6808.1866
Deduct 450 from 500 and we're left with 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 quotient of the division is 6808.1866, and the remainder is 0.0005.