336557 ÷ 9 
Let's see how many times 9 fits into 336557.

Going ahead to step 1:
9 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 9

Let's proceed to step 2:
If we divide 33 by 9, we get 3 and a remainder of 6.
Use 3 as the next digit of our solution. 
Result so far: 3.0
If we take 27 away from 33, we end up with 6.
Fetch the next digit (6) from the dividend, attach it to 6 and continue: 66 / 9

Moving on to step 3:
9 can be fit into 66 7 times, resulting in a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 37.0
Subtract 63 from 66 to get 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 9

Going ahead to step 4:
9 goes into 35 3 times with a remainder of 8.
The next digit of our result is 3. 
Result so far: 373.0
If we subtract 27 from 35, we get 8.
Take the next digit (5) from the dividend and append it to 8, then repeat: 85 / 9

Let's proceed to step 5:
If we divide 85 by 9, we get 9 and a remainder of 4.
Record the quotient 9 as the next digit in the result. 
Result so far: 3739.0
If we take 81 away from 85, we end up with 4.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 9

Going ahead to step 6:
47 divided by 9 is 5 with a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 37395.0
The remainder is 2 after subtracting 45 from 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 7:
The number 9 fits into 20 2 times, leaving a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 37395.2
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
9 can be fit into 20 2 times, resulting in a remainder of 2.
The next digit of our result is 2. 
Result so far: 37395.22
Deduct 18 from 20 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 37395.22 and a remainder of 0.002.