821781 ÷ 65 
We want to figure out the number of times 821781 can be divided by 65.

On to step 1:
65 goes into 8 0 times with a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Grab the next digit (2) from the dividend, add it to 8, then carry on: 82 / 65

On to step 2:
65 goes into 82 1 times with a remainder of 17.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 17 after subtracting 65 from 82.
Fetch the next digit (1) from the dividend, attach it to 17 and continue: 171 / 65

Going ahead to step 3:
65 can be fit into 171 2 times, resulting in a remainder of 41.
Use 2 as the next digit of our solution. 
Result so far: 12.0
If we subtract 130 from 171, we get 41.
Bring next digit (7) of the dividend behind the 41 and repeat the process: 417 / 65

Step 4:
If we divide 417 by 65, we get 6 and a remainder of 27.
Use 6 as the next digit of our solution. 
Result so far: 126.0
If we take 390 away from 417, we end up with 27.
Bring next digit (8) of the dividend behind the 27 and repeat the process: 278 / 65

Step 5:
If we divide 278 by 65, we get 4 and a remainder of 18.
Record the quotient 4 as the next digit in the result. 
Result so far: 1264.0
Subtracting 260 from 278 leaves us with 18.
Fetch the next digit (1) from the dividend, attach it to 18 and continue: 181 / 65

Advancing to step 6:
65 goes into 181 2 times with a remainder of 51.
Write down 2 as next digit of the result. 
Result so far: 12642.0
Subtracting 130 from 181 leaves us with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Going ahead to step 7:
65 can be fit into 510 7 times, resulting in a remainder of 55.
Record the quotient 7 as the next digit in the result. 
Result so far: 12642.7
If we subtract 455 from 510, we get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

On to step 8:
65 can be fit into 550 8 times, resulting in a remainder of 30.
The next digit of our result is 8. 
Result so far: 12642.78
The remainder is 30 after subtracting 520 from 550.
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 9:
When dividing 300 by 65, we get 4 with a remainder of 40.
The number 4 becomes the next digit in our result. 
Result so far: 12642.784
Subtract 260 from 300 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 10:
400 divided by 65 is 6 with a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 12642.7846
The remainder is 10 after subtracting 390 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 11:
The number 65 fits into 100 1 times, leaving a remainder of 35.
Put 1 as the next digit of the answer. 
Result so far: 12642.78461
Subtracting 65 from 100 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 12:
The number 65 fits into 350 5 times, leaving a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 12642.784615
If we subtract 325 from 350, 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.

Let's proceed to step 13:
250 divided by 65 is 3 with a remainder of 55.
Write down 3 as next digit of the result. 
Result so far: 12642.7846153
The remainder is 55 after subtracting 195 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 14:
If we divide 550 by 65, we get 8 and a remainder of 30.
Record the quotient 8 as the next digit in the result. 
Result so far: 12642.78461538
Subtracting 520 from 550 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.

The quotient of the division is 12642.78461538, and the remainder is 3e-08.