We're dividing 413659 by 3 
Our goal is to divide 413659 by 3.

Let's proceed to step 1:
The number 3 fits into 4 1 times, leaving a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 3 away from 4, we end up with 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 3

Going ahead to step 2:
When dividing 11 by 3, we get 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 9 away from 11, we end up with 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 3

Let's proceed to step 3:
When dividing 23 by 3, we get 7 with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 137.0
If we subtract 21 from 23, we get 2.
Append the next digit (6) from the dividend to 2 and continue with: 26 / 3

Advancing to step 4:
26 divided by 3 is 8 with a remainder of 2.
The next digit of our result is 8. 
Result so far: 1378.0
The remainder is 2 after subtracting 24 from 26.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 3

On to step 5:
If we divide 25 by 3, we get 8 and a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 13788.0
If we subtract 24 from 25, we get 1.
Append the next digit (9) from the dividend to 1 and continue with: 19 / 3

Moving on to step 6:
19 divided by 3 is 6 with a remainder of 1.
The number 6 becomes the next digit in our result. 
Result so far: 137886.0
If we take 18 away from 19, 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.

Going ahead to step 7:
3 can be fit into 10 3 times, resulting in a remainder of 1.
The next digit of our result is 3. 
Result so far: 137886.3
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.

Step 8:
10 divided by 3 is 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 137886.33
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.

The quotient of the division is 137886.33, and the remainder is 0.001.