We look at the division of 821312 by 77 
Our goal is to divide 821312 by 77.

Step 1:
If we divide 8 by 77, we get 0 and a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Include the next digit (2) from the dividend after 8, then repeat: 82 / 77

Moving on to step 2:
When dividing 82 by 77, we get 1 with a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 77 away from 82, we end up with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 77

Advancing to step 3:
77 goes into 51 0 times with a remainder of 51.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we take 0 away from 51, we end up with 51.
Bring next digit (3) of the dividend behind the 51 and repeat the process: 513 / 77

On to step 4:
77 goes into 513 6 times with a remainder of 51.
Put 6 as the next digit of the answer. 
Result so far: 106.0
Subtract 462 from 513 to get 51.
Grab the next digit (1) from the dividend, add it to 51, then carry on: 511 / 77

Step 5:
The number 77 fits into 511 6 times, leaving a remainder of 49.
Write down 6 as next digit of the result. 
Result so far: 1066.0
The remainder is 49 after subtracting 462 from 511.
Append the next digit (2) from the dividend to 49 and continue with: 492 / 77

Advancing to step 6:
If we divide 492 by 77, we get 6 and a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 10666.0
The remainder is 30 after subtracting 462 from 492.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 7:
If we divide 300 by 77, we get 3 and a remainder of 69.
Record the quotient 3 as the next digit in the result. 
Result so far: 10666.3
Deduct 231 from 300 and we're left with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Let's proceed to step 8:
690 divided by 77 is 8 with a remainder of 74.
Record the quotient 8 as the next digit in the result. 
Result so far: 10666.38
Deduct 616 from 690 and we're left with 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Step 9:
740 divided by 77 is 9 with a remainder of 47.
The next digit of our result is 9. 
Result so far: 10666.389
If we take 693 away from 740, we end up with 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

On to step 10:
77 can be fit into 470 6 times, resulting in a remainder of 8.
Use 6 as the next digit of our solution. 
Result so far: 10666.3896
Subtract 462 from 470 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 11:
When dividing 80 by 77, we get 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 10666.38961
Subtract 77 from 80 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 12:
30 divided by 77 is 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 10666.38961
Subtracting 0 from 30 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 13:
77 goes into 300 3 times with a remainder of 69.
Use 3 as the next digit of our solution. 
Result so far: 10666.3896103
If we subtract 231 from 300, we get 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Let's proceed to step 14:
690 divided by 77 is 8 with a remainder of 74.
Use 8 as the next digit of our solution. 
Result so far: 10666.38961038
Subtract 616 from 690 to get 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Our division results in 10666.38961038 with a remaining 7.4e-08.