We're dividing 410584 by 3 
We're looking to find how many times 3 goes into 410584.

Step 1:
The number 3 fits into 4 1 times, leaving a remainder of 1.
The next digit of our result is 1. 
Result so far: 1.0
If we take 3 away from 4, we end up with 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 3

Moving on to step 2:
3 goes into 11 3 times with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
Deduct 9 from 11 and we're left with 2.
Grab the next digit (0) from the dividend, add it to 2, then carry on: 20 / 3

Advancing to step 3:
When dividing 20 by 3, we get 6 with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 136.0
If we take 18 away from 20, we end up with 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 3

Advancing to step 4:
25 divided by 3 is 8 with a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 1368.0
Subtract 24 from 25 to get 1.
Take the next digit (8) from the dividend and append it to 1, then repeat: 18 / 3

Step 5:
3 can be fit into 18 6 times, resulting in a remainder of 0.
The number 6 becomes the next digit in our result. 
Result so far: 13686.0
If we take 18 away from 18, we end up with 0.
Include the next digit (4) from the dividend after 0, then repeat: 4 / 3

On to step 6:
3 goes into 4 1 times with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 136861.0
Subtract 3 from 4 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
3 can be fit into 10 3 times, resulting in a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 136861.3
If we subtract 9 from 10, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 8:
The number 3 fits into 10 3 times, leaving a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 136861.33
If we take 9 away from 10, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 136861.33 with a balance of 0.001.