We're dividing 821826 by 65 
We want to figure out the number of times 821826 can be divided by 65.

Advancing to step 1:
65 goes into 8 0 times with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 8, we end up with 8.
Take the next digit (2) from the dividend and append it to 8, then repeat: 82 / 65

Advancing to step 2:
82 divided by 65 is 1 with a remainder of 17.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 65 from 82, we get 17.
Take the next digit (1) from the dividend and append it to 17, then repeat: 171 / 65

Step 3:
When dividing 171 by 65, we get 2 with a remainder of 41.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Deduct 130 from 171 and we're left with 41.
Bring next digit (8) of the dividend behind the 41 and repeat the process: 418 / 65

On to step 4:
The number 65 fits into 418 6 times, leaving a remainder of 28.
The next digit of our result is 6. 
Result so far: 126.0
Deduct 390 from 418 and we're left with 28.
Include the next digit (2) from the dividend after 28, then repeat: 282 / 65

Advancing to step 5:
65 can be fit into 282 4 times, resulting in a remainder of 22.
Put 4 as the next digit of the answer. 
Result so far: 1264.0
Deduct 260 from 282 and we're left with 22.
Bring next digit (6) of the dividend behind the 22 and repeat the process: 226 / 65

Moving on to step 6:
If we divide 226 by 65, we get 3 and a remainder of 31.
The next digit of our result is 3. 
Result so far: 12643.0
Subtracting 195 from 226 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 7:
65 goes into 310 4 times with a remainder of 50.
Write down 4 as next digit of the result. 
Result so far: 12643.4
Deduct 260 from 310 and we're left 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.

On to step 8:
65 goes into 500 7 times with a remainder of 45.
Record the quotient 7 as the next digit in the result. 
Result so far: 12643.47
The remainder is 45 after subtracting 455 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Step 9:
The number 65 fits into 450 6 times, leaving a remainder of 60.
Put 6 as the next digit of the answer. 
Result so far: 12643.476
If we take 390 away from 450, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 10:
If we divide 600 by 65, we get 9 and a remainder of 15.
Put 9 as the next digit of the answer. 
Result so far: 12643.4769
If we subtract 585 from 600, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 11:
When dividing 150 by 65, we get 2 with a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 12643.47692
Subtracting 130 from 150 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.

Let's proceed to step 12:
If we divide 200 by 65, we get 3 and a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 12643.476923
If we take 195 away from 200, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 13:
When dividing 50 by 65, we get 0 with a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 12643.476923
If we take 0 away from 50, we end up 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.

Advancing to step 14:
When dividing 500 by 65, we get 7 with a remainder of 45.
Record the quotient 7 as the next digit in the result. 
Result so far: 12643.47692307
Subtract 455 from 500 to get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

In conclusion, the division gives 12643.47692307 with a balance of 4.5e-08.