We look at the division of 509822 by 65 
We want to figure out the number of times 509822 can be divided by 65.

Let's proceed to step 1:
65 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 65

Let's proceed to step 2:
If we divide 50 by 65, we get 0 and a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 50 after subtracting 0 from 50.
Grab the next digit (9) from the dividend, add it to 50, then carry on: 509 / 65

On to step 3:
The number 65 fits into 509 7 times, leaving a remainder of 54.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtract 455 from 509 to get 54.
Bring next digit (8) of the dividend behind the 54 and repeat the process: 548 / 65

Advancing to step 4:
The number 65 fits into 548 8 times, leaving a remainder of 28.
Put 8 as the next digit of the answer. 
Result so far: 78.0
Subtract 520 from 548 to get 28.
Append the next digit (2) from the dividend to 28 and continue with: 282 / 65

Step 5:
282 divided by 65 is 4 with a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 784.0
Deduct 260 from 282 and we're left with 22.
Grab the next digit (2) from the dividend, add it to 22, then carry on: 222 / 65

Advancing to step 6:
65 goes into 222 3 times with a remainder of 27.
Put 3 as the next digit of the answer. 
Result so far: 7843.0
The remainder is 27 after subtracting 195 from 222.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Moving on to step 7:
If we divide 270 by 65, we get 4 and a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 7843.4
The remainder is 10 after subtracting 260 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
65 goes into 100 1 times with a remainder of 35.
The number 1 becomes the next digit in our result. 
Result so far: 7843.41
The remainder is 35 after subtracting 65 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 9:
65 can be fit into 350 5 times, resulting in a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 7843.415
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.

On to step 10:
250 divided by 65 is 3 with a remainder of 55.
The number 3 becomes the next digit in our result. 
Result so far: 7843.4153
If we take 195 away from 250, we end up with 55.
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 11:
If we divide 550 by 65, we get 8 and a remainder of 30.
Write down 8 as next digit of the result. 
Result so far: 7843.41538
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.

Let's proceed to step 12:
The number 65 fits into 300 4 times, leaving a remainder of 40.
The next digit of our result is 4. 
Result so far: 7843.415384
If we take 260 away from 300, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 13:
65 goes into 400 6 times with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 7843.4153846
Subtract 390 from 400 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 14:
100 divided by 65 is 1 with a remainder of 35.
The next digit of our result is 1. 
Result so far: 7843.41538461
If we subtract 65 from 100, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

The quotient of the division is 7843.41538461, and the remainder is 3.5e-08.