We're dividing 472259 by 3 
We're looking to find how many times 3 goes into 472259.

Moving on to step 1:
If we divide 4 by 3, we get 1 and a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 1 after subtracting 3 from 4.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 3

Going ahead to step 2:
17 divided by 3 is 5 with a remainder of 2.
The next digit of our result is 5. 
Result so far: 15.0
Deduct 15 from 17 and we're left with 2.
Include the next digit (2) from the dividend after 2, then repeat: 22 / 3

Step 3:
3 goes into 22 7 times with a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 157.0
The remainder is 1 after subtracting 21 from 22.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 3

Let's proceed to step 4:
When dividing 12 by 3, we get 4 with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 1574.0
Subtracting 12 from 12 leaves us with 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 3

Moving on to step 5:
When dividing 5 by 3, we get 1 with a remainder of 2.
The next digit of our result is 1. 
Result so far: 15741.0
If we take 3 away from 5, we end up with 2.
Include the next digit (9) from the dividend after 2, then repeat: 29 / 3

Advancing to step 6:
29 divided by 3 is 9 with a remainder of 2.
Write down 9 as next digit of the result. 
Result so far: 157419.0
Subtract 27 from 29 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 7:
3 can be fit into 20 6 times, resulting in a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 157419.6
Subtracting 18 from 20 leaves us 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 goes into 20 6 times with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 157419.66
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.

The final result is 157419.66 with a remainder of 0.002.