We're dividing 577337 by 3 
We're looking to find how many times 3 goes into 577337.

Moving on to step 1:
The number 3 fits into 5 1 times, leaving a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 3 from 5 to get 2.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 3

Moving on to step 2:
When dividing 27 by 3, we get 9 with a remainder of 0.
The number 9 becomes the next digit in our result. 
Result so far: 19.0
If we take 27 away from 27, we end up with 0.
Take the next digit (7) from the dividend and append it to 0, then repeat: 7 / 3

Moving on to step 3:
3 can be fit into 7 2 times, resulting in a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 192.0
Subtract 6 from 7 to get 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 3

Let's proceed to step 4:
13 divided by 3 is 4 with a remainder of 1.
The number 4 becomes the next digit in our result. 
Result so far: 1924.0
The remainder is 1 after subtracting 12 from 13.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 3

Moving on to step 5:
3 can be fit into 13 4 times, resulting in a remainder of 1.
The next digit of our result is 4. 
Result so far: 19244.0
If we take 12 away from 13, we end up with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 3

Let's proceed to step 6:
3 can be fit into 17 5 times, resulting in a remainder of 2.
The next digit of our result is 5. 
Result so far: 192445.0
Deduct 15 from 17 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.

Let's proceed to step 7:
3 can be fit into 20 6 times, resulting in a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 192445.6
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.

Let's proceed to step 8:
3 can be fit into 20 6 times, resulting in a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 192445.66
If we take 18 away from 20, we end up 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.

In conclusion, the division gives 192445.66 with a balance of 0.002.