We're dividing 33629 by 46 
We want to figure out the number of times 33629 can be divided by 46.

Advancing to step 1:
46 can be fit into 3 0 times, resulting in a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Include the next digit (3) from the dividend after 3, then repeat: 33 / 46

Going ahead to step 2:
46 can be fit into 33 0 times, resulting in a remainder of 33.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 33, we end up with 33.
Fetch the next digit (6) from the dividend, attach it to 33 and continue: 336 / 46

Let's proceed to step 3:
46 goes into 336 7 times with a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtract 322 from 336 to get 14.
Fetch the next digit (2) from the dividend, attach it to 14 and continue: 142 / 46

Step 4:
If we divide 142 by 46, we get 3 and a remainder of 4.
Put 3 as the next digit of the answer. 
Result so far: 73.0
If we take 138 away from 142, we end up with 4.
Fetch the next digit (9) from the dividend, attach it to 4 and continue: 49 / 46

Moving on to step 5:
46 goes into 49 1 times with a remainder of 3.
The next digit of our result is 1. 
Result so far: 731.0
Subtracting 46 from 49 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 6:
30 divided by 46 is 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 731.0
Subtracting 0 from 30 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 7:
When dividing 300 by 46, we get 6 with a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 731.06
The remainder is 24 after subtracting 276 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 8:
The number 46 fits into 240 5 times, leaving a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 731.065
Subtracting 230 from 240 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 9:
100 divided by 46 is 2 with a remainder of 8.
The next digit of our result is 2. 
Result so far: 731.0652
If we subtract 92 from 100, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 10:
The number 46 fits into 80 1 times, leaving a remainder of 34.
Record the quotient 1 as the next digit in the result. 
Result so far: 731.06521
Deduct 46 from 80 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 11:
46 goes into 340 7 times with a remainder of 18.
The number 7 becomes the next digit in our result. 
Result so far: 731.065217
The remainder is 18 after subtracting 322 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 12:
46 can be fit into 180 3 times, resulting in a remainder of 42.
Record the quotient 3 as the next digit in the result. 
Result so far: 731.0652173
The remainder is 42 after subtracting 138 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 13:
46 can be fit into 420 9 times, resulting in a remainder of 6.
Use 9 as the next digit of our solution. 
Result so far: 731.06521739
If we take 414 away from 420, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Our division results in 731.06521739 with a remaining 6e-09.