We're dividing 476174 by 3 
We want to divide 476174 by 3.

Let's proceed to step 1:
The number 3 fits into 4 1 times, leaving a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 3 from 4 and we're left with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 3

Let's proceed to step 2:
If we divide 17 by 3, we get 5 and a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 15.0
If we take 15 away from 17, we end up with 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 3

Let's proceed to step 3:
3 goes into 26 8 times with a remainder of 2.
The next digit of our result is 8. 
Result so far: 158.0
Subtract 24 from 26 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 3

Moving on to step 4:
3 goes into 21 7 times with a remainder of 0.
The number 7 becomes the next digit in our result. 
Result so far: 1587.0
Subtract 21 from 21 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 3

Moving on to step 5:
If we divide 7 by 3, we get 2 and a remainder of 1.
The number 2 becomes the next digit in our result. 
Result so far: 15872.0
If we take 6 away from 7, we end up with 1.
Append the next digit (4) from the dividend to 1 and continue with: 14 / 3

Going ahead to step 6:
3 goes into 14 4 times with a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 158724.0
If we subtract 12 from 14, we 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.

Moving on to step 7:
20 divided by 3 is 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 158724.6
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:
If we divide 20 by 3, we get 6 and a remainder of 2.
The next digit of our result is 6. 
Result so far: 158724.66
Subtract 18 from 20 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.

The final result is 158724.66 with a remainder of 0.002.