353663 divided by 44 
We're looking to find how many times 44 goes into 353663.

Moving on to step 1:
3 divided by 44 is 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 44

Going ahead to step 2:
If we divide 35 by 44, we get 0 and a remainder of 35.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 35, we end up with 35.
Take the next digit (3) from the dividend and append it to 35, then repeat: 353 / 44

On to step 3:
The number 44 fits into 353 8 times, leaving a remainder of 1.
Use 8 as the next digit of our solution. 
Result so far: 8.0
If we take 352 away from 353, we end up with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 44

Advancing to step 4:
44 can be fit into 16 0 times, resulting in a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 80.0
Subtracting 0 from 16 leaves us with 16.
Bring next digit (6) of the dividend behind the 16 and repeat the process: 166 / 44

Step 5:
44 can be fit into 166 3 times, resulting in a remainder of 34.
The next digit of our result is 3. 
Result so far: 803.0
Subtract 132 from 166 to get 34.
Grab the next digit (3) from the dividend, add it to 34, then carry on: 343 / 44

Going ahead to step 6:
44 goes into 343 7 times with a remainder of 35.
Use 7 as the next digit of our solution. 
Result so far: 8037.0
If we subtract 308 from 343, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 7:
The number 44 fits into 350 7 times, leaving a remainder of 42.
The number 7 becomes the next digit in our result. 
Result so far: 8037.7
Deduct 308 from 350 and we're left with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Step 8:
420 divided by 44 is 9 with a remainder of 24.
Put 9 as the next digit of the answer. 
Result so far: 8037.79
Subtracting 396 from 420 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 9:
44 can be fit into 240 5 times, resulting in a remainder of 20.
The number 5 becomes the next digit in our result. 
Result so far: 8037.795
The remainder is 20 after subtracting 220 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 10:
44 goes into 200 4 times with a remainder of 24.
Record the quotient 4 as the next digit in the result. 
Result so far: 8037.7954
Subtracting 176 from 200 leaves us with 24.
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 11:
240 divided by 44 is 5 with a remainder of 20.
Use 5 as the next digit of our solution. 
Result so far: 8037.79545
Subtract 220 from 240 to get 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 12:
44 can be fit into 200 4 times, resulting in a remainder of 24.
Put 4 as the next digit of the answer. 
Result so far: 8037.795454
If we subtract 176 from 200, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 13:
44 can be fit into 240 5 times, resulting in a remainder of 20.
The next digit of our result is 5. 
Result so far: 8037.7954545
If we subtract 220 from 240, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 14:
44 can be fit into 200 4 times, resulting in a remainder of 24.
The next digit of our result is 4. 
Result so far: 8037.79545454
If we subtract 176 from 200, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The final outcome is 8037.79545454, with a leftover of 2.4e-08.