137566 divided by 18 
Our goal is to divide 137566 by 18.

Advancing to step 1:
18 goes into 1 0 times with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 18

Let's proceed to step 2:
When dividing 13 by 18, we get 0 with a remainder of 13.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 13, we end up with 13.
Bring next digit (7) of the dividend behind the 13 and repeat the process: 137 / 18

Moving on to step 3:
When dividing 137 by 18, we get 7 with a remainder of 11.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtracting 126 from 137 leaves us with 11.
Grab the next digit (5) from the dividend, add it to 11, then carry on: 115 / 18

Going ahead to step 4:
115 divided by 18 is 6 with a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 76.0
If we subtract 108 from 115, we get 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 18

Step 5:
If we divide 76 by 18, we get 4 and a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 764.0
Deduct 72 from 76 and we're left with 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 18

On to step 6:
18 can be fit into 46 2 times, resulting in a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 7642.0
If we subtract 36 from 46, 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.

Let's proceed to step 7:
18 can be fit into 100 5 times, resulting in a remainder of 10.
The next digit of our result is 5. 
Result so far: 7642.5
Subtract 90 from 100 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 8:
When dividing 100 by 18, we get 5 with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 7642.55
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.

The quotient of the division is 7642.55, and the remainder is 0.01.