Let's divide 171986 by 15
Our goal is to divide 171986 by 15.

Advancing to step 1:
1 divided by 15 is 0 with 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.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 15

Moving on to step 2:
15 goes into 17 1 times with a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 15 from 17, we get 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 15

Advancing to step 3:
The number 15 fits into 21 1 times, leaving a remainder of 6.
The next digit of our result is 1. 
Result so far: 11.0
Subtracting 15 from 21 leaves us with 6.
Fetch the next digit (9) from the dividend, attach it to 6 and continue: 69 / 15

Step 4:
When dividing 69 by 15, we get 4 with a remainder of 9.
The next digit of our result is 4. 
Result so far: 114.0
Subtracting 60 from 69 leaves us with 9.
Append the next digit (8) from the dividend to 9 and continue with: 98 / 15

Advancing to step 5:
The number 15 fits into 98 6 times, leaving a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 1146.0
Deduct 90 from 98 and we're left with 8.
Include the next digit (6) from the dividend after 8, then repeat: 86 / 15

Moving on to step 6:
15 can be fit into 86 5 times, resulting in a remainder of 11.
Use 5 as the next digit of our solution. 
Result so far: 11465.0
Deduct 75 from 86 and we're left 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.

Advancing to step 7:
If we divide 110 by 15, we get 7 and a remainder of 5.
Use 7 as the next digit of our solution. 
Result so far: 11465.7
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.

On to step 8:
When dividing 50 by 15, we get 3 with a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 11465.73
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.

Moving on to step 9:
If we divide 50 by 15, we get 3 and a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 11465.733
Subtracting 45 from 50 leaves us 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.

The quotient of the division is 11465.733, and the remainder is 0.0005.