We look at the division of 12597 by 15 
We're looking to find how many times 15 goes into 12597.

Going ahead to step 1:
15 goes into 1 0 times with 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.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 15

Going ahead to step 2:
15 can be fit into 12 0 times, resulting in a remainder of 12.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 12, we get 12.
Fetch the next digit (5) from the dividend, attach it to 12 and continue: 125 / 15

Going ahead to step 3:
125 divided by 15 is 8 with a remainder of 5.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
If we subtract 120 from 125, we get 5.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 15

Moving on to step 4:
If we divide 59 by 15, we get 3 and a remainder of 14.
Record the quotient 3 as the next digit in the result. 
Result so far: 83.0
Subtract 45 from 59 to get 14.
Bring next digit (7) of the dividend behind the 14 and repeat the process: 147 / 15

Step 5:
If we divide 147 by 15, we get 9 and a remainder of 12.
Record the quotient 9 as the next digit in the result. 
Result so far: 839.0
If we subtract 135 from 147, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 6:
120 divided by 15 is 8 with a remainder of 0.
Write down 8 as next digit of the result. 
Result so far: 839.8
If we subtract 120 from 120, we 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.

On to step 7:
15 can be fit into 0 0 times, resulting in a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 839.8
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.

Let's proceed to step 8:
When dividing 0 by 15, we get 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 839.8
Deduct 0 from 0 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.

The final outcome is 839.8, with a leftover of 0.0.