We look at the division of 113171 by 15 
Our goal is to divide 113171 by 15.

Advancing to step 1:
1 divided by 15 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 15

Moving on to step 2:
When dividing 11 by 15, we get 0 with a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 11, we end up with 11.
Grab the next digit (3) from the dividend, add it to 11, then carry on: 113 / 15

Going ahead to step 3:
15 can be fit into 113 7 times, resulting in a remainder of 8.
Write down 7 as next digit of the result. 
Result so far: 7.0
Subtract 105 from 113 to get 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 15

On to step 4:
15 can be fit into 81 5 times, resulting in a remainder of 6.
Use 5 as the next digit of our solution. 
Result so far: 75.0
The remainder is 6 after subtracting 75 from 81.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 15

Let's proceed to step 5:
15 goes into 67 4 times with a remainder of 7.
The number 4 becomes the next digit in our result. 
Result so far: 754.0
Subtract 60 from 67 to get 7.
Take the next digit (1) from the dividend and append it to 7, then repeat: 71 / 15

Going ahead to step 6:
When dividing 71 by 15, we get 4 with a remainder of 11.
The next digit of our result is 4. 
Result so far: 7544.0
If we take 60 away from 71, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 7:
If we divide 110 by 15, we get 7 and a remainder of 5.
Write down 7 as next digit of the result. 
Result so far: 7544.7
Deduct 105 from 110 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 8:
If we divide 50 by 15, we get 3 and a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 7544.73
If we subtract 45 from 50, 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.

Step 9:
If we divide 50 by 15, we get 3 and a remainder of 5.
Record the quotient 3 as the next digit in the result. 
Result so far: 7544.733
Subtract 45 from 50 to 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.

The quotient of the division is 7544.733, and the remainder is 0.0005.