180665 ÷ 13 
Our goal is to divide 180665 by 13.

Advancing to step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (8) from the dividend, add it to 1, then carry on: 18 / 13

Advancing to step 2:
13 can be fit into 18 1 times, resulting in a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 13 from 18 leaves us with 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 13

Going ahead to step 3:
50 divided by 13 is 3 with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
Deduct 39 from 50 and we're left with 11.
Fetch the next digit (6) from the dividend, attach it to 11 and continue: 116 / 13

Step 4:
When dividing 116 by 13, we get 8 with a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 138.0
Subtracting 104 from 116 leaves us with 12.
Include the next digit (6) from the dividend after 12, then repeat: 126 / 13

Moving on to step 5:
13 goes into 126 9 times with a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 1389.0
Deduct 117 from 126 and we're left with 9.
Include the next digit (5) from the dividend after 9, then repeat: 95 / 13

On to step 6:
13 goes into 95 7 times with a remainder of 4.
Record the quotient 7 as the next digit in the result. 
Result so far: 13897.0
If we take 91 away from 95, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
If we divide 40 by 13, we get 3 and a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 13897.3
Subtracting 39 from 40 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 8:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 13897.3
If we subtract 0 from 10, 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.

Advancing to step 9:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 13897.307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 10:
90 divided by 13 is 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 13897.3076
Subtract 78 from 90 to 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 11:
When dividing 120 by 13, we get 9 with a remainder of 3.
The next digit of our result is 9. 
Result so far: 13897.30769
Deduct 117 from 120 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 12:
When dividing 30 by 13, we get 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 13897.307692
Subtract 26 from 30 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 13:
When dividing 40 by 13, we get 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 13897.3076923
If we take 39 away from 40, we end up 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.

Advancing to step 14:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 13897.3076923
Deduct 0 from 10 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.

The final result is 13897.3076923 with a remainder of 1e-08.