We're dividing 579242 by 75 
We want to figure out the number of times 579242 can be divided by 75.

Advancing to step 1:
5 divided by 75 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 75

Moving on to step 2:
57 divided by 75 is 0 with a remainder of 57.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 57 and we're left with 57.
Append the next digit (9) from the dividend to 57 and continue with: 579 / 75

On to step 3:
579 divided by 75 is 7 with a remainder of 54.
Put 7 as the next digit of the answer. 
Result so far: 7.0
The remainder is 54 after subtracting 525 from 579.
Bring next digit (2) of the dividend behind the 54 and repeat the process: 542 / 75

Let's proceed to step 4:
The number 75 fits into 542 7 times, leaving a remainder of 17.
Write down 7 as next digit of the result. 
Result so far: 77.0
If we take 525 away from 542, we end up with 17.
Include the next digit (4) from the dividend after 17, then repeat: 174 / 75

On to step 5:
75 can be fit into 174 2 times, resulting in a remainder of 24.
Record the quotient 2 as the next digit in the result. 
Result so far: 772.0
Deduct 150 from 174 and we're left with 24.
Include the next digit (2) from the dividend after 24, then repeat: 242 / 75

Moving on to step 6:
75 goes into 242 3 times with a remainder of 17.
Record the quotient 3 as the next digit in the result. 
Result so far: 7723.0
If we subtract 225 from 242, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 7:
75 goes into 170 2 times with a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 7723.2
Subtracting 150 from 170 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 8:
When dividing 200 by 75, we get 2 with a remainder of 50.
The next digit of our result is 2. 
Result so far: 7723.22
Subtracting 150 from 200 leaves us 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 7723.22, and the remainder is 0.05.