We look at the division of 77821 by 75 
We're looking to find how many times 75 goes into 77821.

Advancing to step 1:
The number 75 fits into 7 0 times, leaving a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 75

Step 2:
If we divide 77 by 75, we get 1 and a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 2 after subtracting 75 from 77.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 75

On to step 3:
If we divide 28 by 75, we get 0 and a remainder of 28.
Write down 0 as next digit of the result. 
Result so far: 10.0
If we subtract 0 from 28, we get 28.
Include the next digit (2) from the dividend after 28, then repeat: 282 / 75

Let's proceed to step 4:
75 can be fit into 282 3 times, resulting in a remainder of 57.
The number 3 becomes the next digit in our result. 
Result so far: 103.0
Deduct 225 from 282 and we're left with 57.
Take the next digit (1) from the dividend and append it to 57, then repeat: 571 / 75

Let's proceed to step 5:
75 goes into 571 7 times with a remainder of 46.
Put 7 as the next digit of the answer. 
Result so far: 1037.0
If we subtract 525 from 571, we get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 6:
75 goes into 460 6 times with a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 1037.6
Subtracting 450 from 460 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 7:
75 goes into 100 1 times with a remainder of 25.
The number 1 becomes the next digit in our result. 
Result so far: 1037.61
Subtracting 75 from 100 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.

Advancing to step 8:
When dividing 250 by 75, we get 3 with a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 1037.613
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 9:
The number 75 fits into 250 3 times, leaving a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 1037.6133
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.

The quotient of the division is 1037.6133, and the remainder is 0.00025.