Let's divide 824122 by 75
We're looking to find how many times 75 goes into 824122.

Going ahead to step 1:
75 can be fit into 8 0 times, resulting in a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Take the next digit (2) from the dividend and append it to 8, then repeat: 82 / 75

Step 2:
82 divided by 75 is 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 75 from 82, we get 7.
Fetch the next digit (4) from the dividend, attach it to 7 and continue: 74 / 75

Moving on to step 3:
The number 75 fits into 74 0 times, leaving a remainder of 74.
Write down 0 as next digit of the result. 
Result so far: 10.0
The remainder is 74 after subtracting 0 from 74.
Append the next digit (1) from the dividend to 74 and continue with: 741 / 75

Moving on to step 4:
75 can be fit into 741 9 times, resulting in a remainder of 66.
Use 9 as the next digit of our solution. 
Result so far: 109.0
If we subtract 675 from 741, we get 66.
Grab the next digit (2) from the dividend, add it to 66, then carry on: 662 / 75

Going ahead to step 5:
If we divide 662 by 75, we get 8 and a remainder of 62.
Record the quotient 8 as the next digit in the result. 
Result so far: 1098.0
If we subtract 600 from 662, we get 62.
Take the next digit (2) from the dividend and append it to 62, then repeat: 622 / 75

Advancing to step 6:
622 divided by 75 is 8 with a remainder of 22.
Put 8 as the next digit of the answer. 
Result so far: 10988.0
The remainder is 22 after subtracting 600 from 622.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 7:
75 can be fit into 220 2 times, resulting in a remainder of 70.
Put 2 as the next digit of the answer. 
Result so far: 10988.2
Subtracting 150 from 220 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

On to step 8:
If we divide 700 by 75, we get 9 and a remainder of 25.
The next digit of our result is 9. 
Result so far: 10988.29
If we subtract 675 from 700, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 9:
250 divided by 75 is 3 with a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 10988.293
Subtracting 225 from 250 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 10:
If we divide 250 by 75, we get 3 and a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 10988.2933
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

After the division, we end up with 10988.2933 and a remainder of 0.00025.