165584 ÷ 11 
Our goal is to divide 165584 by 11.

On to step 1:
If we divide 1 by 11, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 11

Let's proceed to step 2:
When dividing 16 by 11, we get 1 with a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 11 away from 16, we end up with 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 11

Going ahead to step 3:
11 can be fit into 55 5 times, resulting in a remainder of 0.
The next digit of our result is 5. 
Result so far: 15.0
Subtract 55 from 55 to get 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 11

Advancing to step 4:
The number 11 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 150.0
Deduct 0 from 5 and we're left with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 11

Moving on to step 5:
11 can be fit into 58 5 times, resulting in a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 1505.0
The remainder is 3 after subtracting 55 from 58.
Grab the next digit (4) from the dividend, add it to 3, then carry on: 34 / 11

Step 6:
When dividing 34 by 11, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 15053.0
Subtracting 33 from 34 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 7:
10 divided by 11 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 15053.0
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.

Going ahead to step 8:
100 divided by 11 is 9 with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 15053.09
If we take 99 away from 100, 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 9:
The number 11 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 15053.09
Subtract 0 from 10 to 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.

Let's proceed to step 10:
11 goes into 100 9 times with a remainder of 1.
Write down 9 as next digit of the result. 
Result so far: 15053.0909
If we subtract 99 from 100, we get 1.
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 11:
When dividing 10 by 11, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 15053.0909
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.

On to step 12:
The number 11 fits into 100 9 times, leaving a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 15053.090909
If we take 99 away from 100, 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.

Moving on to step 13:
When dividing 10 by 11, we get 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 15053.090909
If we take 0 away from 10, we end up 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.

Going ahead to step 14:
100 divided by 11 is 9 with a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 15053.09090909
If we subtract 99 from 100, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The quotient of the division is 15053.09090909, and the remainder is 1e-09.