We look at the division of 10965 by 65 
Our goal is to divide 10965 by 65.

Advancing to step 1:
65 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 65

Going ahead to step 2:
The number 65 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 65

Going ahead to step 3:
65 goes into 109 1 times with a remainder of 44.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 65 from 109 leaves us with 44.
Append the next digit (6) from the dividend to 44 and continue with: 446 / 65

Step 4:
The number 65 fits into 446 6 times, leaving a remainder of 56.
Record the quotient 6 as the next digit in the result. 
Result so far: 16.0
If we subtract 390 from 446, we get 56.
Include the next digit (5) from the dividend after 56, then repeat: 565 / 65

Moving on to step 5:
65 goes into 565 8 times with a remainder of 45.
Use 8 as the next digit of our solution. 
Result so far: 168.0
Subtract 520 from 565 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.

Let's proceed to step 6:
When dividing 450 by 65, we get 6 with a remainder of 60.
The next digit of our result is 6. 
Result so far: 168.6
Deduct 390 from 450 and we're left 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 7:
65 can be fit into 600 9 times, resulting in a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 168.69
If we take 585 away from 600, we end up with 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 8:
When dividing 150 by 65, we get 2 with a remainder of 20.
The next digit of our result is 2. 
Result so far: 168.692
The remainder is 20 after subtracting 130 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
When dividing 200 by 65, we get 3 with a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 168.6923
If we subtract 195 from 200, we get 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 10:
65 can be fit into 50 0 times, resulting in a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 168.6923
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.

Step 11:
500 divided by 65 is 7 with a remainder of 45.
Use 7 as the next digit of our solution. 
Result so far: 168.692307
If we subtract 455 from 500, we 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.

Let's proceed to step 12:
65 goes into 450 6 times with a remainder of 60.
The next digit of our result is 6. 
Result so far: 168.6923076
Subtract 390 from 450 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.

Going ahead to step 13:
When dividing 600 by 65, we get 9 with a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 168.69230769
Deduct 585 from 600 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

In conclusion, the division gives 168.69230769 with a balance of 1.5e-08.