We're dividing 91591 by 15 
We want to figure out the number of times 91591 can be divided by 15.

Going ahead to step 1:
15 goes into 9 0 times with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Take the next digit (1) from the dividend and append it to 9, then repeat: 91 / 15

Step 2:
If we divide 91 by 15, we get 6 and a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 6.0
The remainder is 1 after subtracting 90 from 91.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 15

Advancing to step 3:
When dividing 15 by 15, we get 1 with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 61.0
If we subtract 15 from 15, we get 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 15

Step 4:
15 can be fit into 9 0 times, resulting in a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 610.0
Deduct 0 from 9 and we're left with 9.
Append the next digit (1) from the dividend to 9 and continue with: 91 / 15

Advancing to step 5:
When dividing 91 by 15, we get 6 with a remainder of 1.
Record the quotient 6 as the next digit in the result. 
Result so far: 6106.0
The remainder is 1 after subtracting 90 from 91.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 6:
15 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 6106.0
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.

Let's proceed to step 7:
If we divide 100 by 15, we get 6 and a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 6106.06
Deduct 90 from 100 and we're left 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.

Moving on to step 8:
The number 15 fits into 100 6 times, leaving a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 6106.066
If we subtract 90 from 100, we 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.

The final outcome is 6106.066, with a leftover of 0.001.