We're dividing 415271 by 3 
We're looking to find how many times 3 goes into 415271.

Let's proceed to step 1:
3 can be fit into 4 1 times, resulting in a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 1 after subtracting 3 from 4.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 3

Moving on to step 2:
11 divided by 3 is 3 with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
If we take 9 away from 11, we end up with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 3

Let's proceed to step 3:
The number 3 fits into 25 8 times, leaving a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 138.0
If we take 24 away from 25, we end up with 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 3

Moving on 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: 1384.0
Subtract 12 from 12 to get 0.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 3

On to step 5:
When dividing 7 by 3, we get 2 with a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 13842.0
If we subtract 6 from 7, we get 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 3

Let's proceed to step 6:
3 goes into 11 3 times with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 138423.0
Deduct 9 from 11 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.

On to step 7:
3 can be fit into 20 6 times, resulting in a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 138423.6
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.

Advancing to step 8:
The number 3 fits into 20 6 times, leaving a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 138423.66
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.

Our division results in 138423.66 with a remaining 0.002.