We're dividing 559734 by 65 
We're looking to find how many times 65 goes into 559734.

Going ahead to step 1:
5 divided by 65 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 65

Advancing to step 2:
55 divided by 65 is 0 with a remainder of 55.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 55 to get 55.
Fetch the next digit (9) from the dividend, attach it to 55 and continue: 559 / 65

Let's proceed to step 3:
The number 65 fits into 559 8 times, leaving a remainder of 39.
The next digit of our result is 8. 
Result so far: 8.0
Deduct 520 from 559 and we're left with 39.
Bring next digit (7) of the dividend behind the 39 and repeat the process: 397 / 65

On to step 4:
397 divided by 65 is 6 with a remainder of 7.
Put 6 as the next digit of the answer. 
Result so far: 86.0
Deduct 390 from 397 and we're left with 7.
Take the next digit (3) from the dividend and append it to 7, then repeat: 73 / 65

Step 5:
When dividing 73 by 65, we get 1 with a remainder of 8.
Use 1 as the next digit of our solution. 
Result so far: 861.0
Deduct 65 from 73 and we're left with 8.
Take the next digit (4) from the dividend and append it to 8, then repeat: 84 / 65

Let's proceed to step 6:
65 goes into 84 1 times with a remainder of 19.
Record the quotient 1 as the next digit in the result. 
Result so far: 8611.0
Subtract 65 from 84 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 7:
65 goes into 190 2 times with a remainder of 60.
Put 2 as the next digit of the answer. 
Result so far: 8611.2
Subtract 130 from 190 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Let's proceed to step 8:
65 can be fit into 600 9 times, resulting in a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 8611.29
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.

Advancing to step 9:
150 divided by 65 is 2 with a remainder of 20.
Put 2 as the next digit of the answer. 
Result so far: 8611.292
If we take 130 away from 150, 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.

On to step 10:
200 divided by 65 is 3 with a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 8611.2923
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.

Step 11:
When dividing 50 by 65, we get 0 with a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 8611.2923
If we subtract 0 from 50, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 12:
500 divided by 65 is 7 with a remainder of 45.
The next digit of our result is 7. 
Result so far: 8611.292307
If we take 455 away from 500, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 13:
65 goes into 450 6 times with a remainder of 60.
Put 6 as the next digit of the answer. 
Result so far: 8611.2923076
If we subtract 390 from 450, we get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Let's proceed to step 14:
If we divide 600 by 65, we get 9 and a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 8611.29230769
Subtract 585 from 600 to 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.

The final outcome is 8611.29230769, with a leftover of 1.5e-08.