We're dividing 115321 by 15 
We're looking to find how many times 15 goes into 115321.

Step 1:
15 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 15

Going ahead to step 2:
11 divided by 15 is 0 with a remainder of 11.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 11 to get 11.
Take the next digit (5) from the dividend and append it to 11, then repeat: 115 / 15

Advancing to step 3:
When dividing 115 by 15, we get 7 with a remainder of 10.
Use 7 as the next digit of our solution. 
Result so far: 7.0
If we subtract 105 from 115, we get 10.
Grab the next digit (3) from the dividend, add it to 10, then carry on: 103 / 15

Advancing to step 4:
The number 15 fits into 103 6 times, leaving a remainder of 13.
The next digit of our result is 6. 
Result so far: 76.0
If we take 90 away from 103, we end up with 13.
Append the next digit (2) from the dividend to 13 and continue with: 132 / 15

Going ahead to step 5:
132 divided by 15 is 8 with a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 768.0
Subtract 120 from 132 to get 12.
Grab the next digit (1) from the dividend, add it to 12, then carry on: 121 / 15

On to step 6:
15 can be fit into 121 8 times, resulting in a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 7688.0
Subtracting 120 from 121 leaves us 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.

Let's proceed to step 7:
15 goes into 10 0 times with a remainder of 10.
The next digit of our result is 0. 
Result so far: 7688.0
Subtracting 0 from 10 leaves us 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 8:
When dividing 100 by 15, we get 6 with a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 7688.06
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.

Going ahead to step 9:
When dividing 100 by 15, we get 6 with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 7688.066
Subtracting 90 from 100 leaves us 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.

After the division, we end up with 7688.066 and a remainder of 0.001.