557417 ÷ 44 
We're looking to find how many times 44 goes into 557417.

Advancing to step 1:
44 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 44

Moving on to step 2:
55 divided by 44 is 1 with a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 44 from 55, we get 11.
Take the next digit (7) from the dividend and append it to 11, then repeat: 117 / 44

Going ahead to step 3:
If we divide 117 by 44, we get 2 and a remainder of 29.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
Subtract 88 from 117 to get 29.
Append the next digit (4) from the dividend to 29 and continue with: 294 / 44

Advancing to step 4:
44 goes into 294 6 times with a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 126.0
If we take 264 away from 294, we end up with 30.
Fetch the next digit (1) from the dividend, attach it to 30 and continue: 301 / 44

Going ahead to step 5:
44 can be fit into 301 6 times, resulting in a remainder of 37.
Record the quotient 6 as the next digit in the result. 
Result so far: 1266.0
If we take 264 away from 301, we end up with 37.
Append the next digit (7) from the dividend to 37 and continue with: 377 / 44

Going ahead to step 6:
44 can be fit into 377 8 times, resulting in a remainder of 25.
Use 8 as the next digit of our solution. 
Result so far: 12668.0
Subtracting 352 from 377 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 7:
44 can be fit into 250 5 times, resulting in a remainder of 30.
The number 5 becomes the next digit in our result. 
Result so far: 12668.5
If we take 220 away from 250, we end up 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.

On to step 8:
44 can be fit into 300 6 times, resulting in a remainder of 36.
Record the quotient 6 as the next digit in the result. 
Result so far: 12668.56
If we subtract 264 from 300, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Let's proceed to step 9:
360 divided by 44 is 8 with a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 12668.568
The remainder is 8 after subtracting 352 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 10:
44 can be fit into 80 1 times, resulting in a remainder of 36.
Record the quotient 1 as the next digit in the result. 
Result so far: 12668.5681
Subtracting 44 from 80 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 11:
44 goes into 360 8 times with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 12668.56818
The remainder is 8 after subtracting 352 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 12:
44 can be fit into 80 1 times, resulting in a remainder of 36.
Record the quotient 1 as the next digit in the result. 
Result so far: 12668.568181
Subtracting 44 from 80 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 13:
When dividing 360 by 44, we get 8 with a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 12668.5681818
Subtract 352 from 360 to 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.

Step 14:
The number 44 fits into 80 1 times, leaving a remainder of 36.
Put 1 as the next digit of the answer. 
Result so far: 12668.56818181
Deduct 44 from 80 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

In conclusion, the division gives 12668.56818181 with a balance of 3.6e-08.