We look at the division of 509565 by 64 
We're looking to find how many times 64 goes into 509565.

Step 1:
The number 64 fits into 5 0 times, leaving a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 64

Going ahead to step 2:
The number 64 fits into 50 0 times, leaving a remainder of 50.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 50 leaves us with 50.
Grab the next digit (9) from the dividend, add it to 50, then carry on: 509 / 64

Moving on to step 3:
When dividing 509 by 64, we get 7 with a remainder of 61.
Put 7 as the next digit of the answer. 
Result so far: 7.0
The remainder is 61 after subtracting 448 from 509.
Include the next digit (5) from the dividend after 61, then repeat: 615 / 64

Going ahead to step 4:
The number 64 fits into 615 9 times, leaving a remainder of 39.
The next digit of our result is 9. 
Result so far: 79.0
Deduct 576 from 615 and we're left with 39.
Append the next digit (6) from the dividend to 39 and continue with: 396 / 64

Let's proceed to step 5:
If we divide 396 by 64, we get 6 and a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 796.0
If we take 384 away from 396, we end up with 12.
Bring next digit (5) of the dividend behind the 12 and repeat the process: 125 / 64

On to step 6:
125 divided by 64 is 1 with a remainder of 61.
Use 1 as the next digit of our solution. 
Result so far: 7961.0
If we subtract 64 from 125, we get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Step 7:
64 can be fit into 610 9 times, resulting in a remainder of 34.
Use 9 as the next digit of our solution. 
Result so far: 7961.9
The remainder is 34 after subtracting 576 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 8:
If we divide 340 by 64, we get 5 and a remainder of 20.
Record the quotient 5 as the next digit in the result. 
Result so far: 7961.95
If we take 320 away from 340, we end up 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 9:
When dividing 200 by 64, we get 3 with a remainder of 8.
Put 3 as the next digit of the answer. 
Result so far: 7961.953
Subtract 192 from 200 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.

On to step 10:
If we divide 80 by 64, we get 1 and a remainder of 16.
Write down 1 as next digit of the result. 
Result so far: 7961.9531
Subtracting 64 from 80 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 11:
When dividing 160 by 64, we get 2 with a remainder of 32.
The number 2 becomes the next digit in our result. 
Result so far: 7961.95312
Deduct 128 from 160 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Going ahead to step 12:
64 can be fit into 320 5 times, resulting in a remainder of 0.
The next digit of our result is 5. 
Result so far: 7961.953125
Deduct 320 from 320 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 13:
64 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 7961.953125
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 14:
The number 64 fits into 0 0 times, leaving a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 7961.953125
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 7961.953125, and the remainder is 0.0.