We're dividing 116596 by 15 
We're looking to find how many times 15 goes into 116596.

Advancing to step 1:
If we divide 1 by 15, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 15

Moving on to step 2:
11 divided by 15 is 0 with a remainder of 11.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 11, we get 11.
Append the next digit (6) from the dividend to 11 and continue with: 116 / 15

Let's proceed to step 3:
15 can be fit into 116 7 times, resulting in a remainder of 11.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we subtract 105 from 116, we get 11.
Include the next digit (5) from the dividend after 11, then repeat: 115 / 15

Moving on to step 4:
If we divide 115 by 15, we get 7 and a remainder of 10.
The next digit of our result is 7. 
Result so far: 77.0
If we take 105 away from 115, we end up with 10.
Include the next digit (9) from the dividend after 10, then repeat: 109 / 15

Step 5:
If we divide 109 by 15, we get 7 and a remainder of 4.
The next digit of our result is 7. 
Result so far: 777.0
Deduct 105 from 109 and we're left with 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 15

Step 6:
15 goes into 46 3 times with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 7773.0
If we take 45 away from 46, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
The number 15 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 7773.0
Subtract 0 from 10 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.

On to step 8:
15 goes into 100 6 times with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 7773.06
If we take 90 away from 100, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 9:
If we divide 100 by 15, we get 6 and a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 7773.066
Subtract 90 from 100 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.

In conclusion, the division gives 7773.066 with a balance of 0.001.