414606 ÷ 33 
We're looking to find how many times 33 goes into 414606.

Going ahead to step 1:
33 can be fit into 4 0 times, resulting in a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 33

Step 2:
If we divide 41 by 33, we get 1 and a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 33 from 41 to get 8.
Take the next digit (4) from the dividend and append it to 8, then repeat: 84 / 33

Going ahead to step 3:
When dividing 84 by 33, we get 2 with a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
If we take 66 away from 84, we end up with 18.
Append the next digit (6) from the dividend to 18 and continue with: 186 / 33

On to step 4:
33 can be fit into 186 5 times, resulting in a remainder of 21.
Record the quotient 5 as the next digit in the result. 
Result so far: 125.0
Subtract 165 from 186 to get 21.
Take the next digit (0) from the dividend and append it to 21, then repeat: 210 / 33

Step 5:
When dividing 210 by 33, we get 6 with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 1256.0
If we take 198 away from 210, we end up with 12.
Take the next digit (6) from the dividend and append it to 12, then repeat: 126 / 33

Going ahead to step 6:
The number 33 fits into 126 3 times, leaving a remainder of 27.
Record the quotient 3 as the next digit in the result. 
Result so far: 12563.0
If we subtract 99 from 126, we get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 7:
33 can be fit into 270 8 times, resulting in a remainder of 6.
The next digit of our result is 8. 
Result so far: 12563.8
Subtract 264 from 270 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 8:
33 goes into 60 1 times with a remainder of 27.
Use 1 as the next digit of our solution. 
Result so far: 12563.81
If we take 33 away from 60, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 9:
33 goes into 270 8 times with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 12563.818
The remainder is 6 after subtracting 264 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 10:
60 divided by 33 is 1 with a remainder of 27.
Put 1 as the next digit of the answer. 
Result so far: 12563.8181
Deduct 33 from 60 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

On to step 11:
The number 33 fits into 270 8 times, leaving a remainder of 6.
The next digit of our result is 8. 
Result so far: 12563.81818
The remainder is 6 after subtracting 264 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 12:
33 goes into 60 1 times with a remainder of 27.
The next digit of our result is 1. 
Result so far: 12563.818181
The remainder is 27 after subtracting 33 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

On to step 13:
33 goes into 270 8 times with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 12563.8181818
Subtract 264 from 270 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 14:
The number 33 fits into 60 1 times, leaving a remainder of 27.
Record the quotient 1 as the next digit in the result. 
Result so far: 12563.81818181
Subtract 33 from 60 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

In conclusion, the division gives 12563.81818181 with a balance of 2.7e-08.