413663 ÷ 30 
We're looking to find how many times 30 goes into 413663.

Step 1:
30 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 30

On to step 2:
The number 30 fits into 41 1 times, leaving a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 30 from 41 leaves us with 11.
Fetch the next digit (3) from the dividend, attach it to 11 and continue: 113 / 30

On to step 3:
30 can be fit into 113 3 times, resulting in a remainder of 23.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we subtract 90 from 113, we get 23.
Bring next digit (6) of the dividend behind the 23 and repeat the process: 236 / 30

Going ahead to step 4:
236 divided by 30 is 7 with a remainder of 26.
The number 7 becomes the next digit in our result. 
Result so far: 137.0
Deduct 210 from 236 and we're left with 26.
Append the next digit (6) from the dividend to 26 and continue with: 266 / 30

Going ahead to step 5:
If we divide 266 by 30, we get 8 and a remainder of 26.
Record the quotient 8 as the next digit in the result. 
Result so far: 1378.0
The remainder is 26 after subtracting 240 from 266.
Include the next digit (3) from the dividend after 26, then repeat: 263 / 30

Advancing to step 6:
30 goes into 263 8 times with a remainder of 23.
The next digit of our result is 8. 
Result so far: 13788.0
The remainder is 23 after subtracting 240 from 263.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 7:
If we divide 230 by 30, we get 7 and a remainder of 20.
Record the quotient 7 as the next digit in the result. 
Result so far: 13788.7
Deduct 210 from 230 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
If we divide 200 by 30, we get 6 and a remainder of 20.
The next digit of our result is 6. 
Result so far: 13788.76
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
When dividing 200 by 30, we get 6 with a remainder of 20.
Put 6 as the next digit of the answer. 
Result so far: 13788.766
Subtracting 180 from 200 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final outcome is 13788.766, with a leftover of 0.002.