We're dividing 660597 by 44 
We're looking to find how many times 44 goes into 660597.

Let's proceed to step 1:
The number 44 fits into 6 0 times, leaving a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 44

Advancing to step 2:
When dividing 66 by 44, we get 1 with a remainder of 22.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 44 away from 66, we end up with 22.
Take the next digit (0) from the dividend and append it to 22, then repeat: 220 / 44

Moving on to step 3:
220 divided by 44 is 5 with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 15.0
The remainder is 0 after subtracting 220 from 220.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 44

Step 4:
If we divide 5 by 44, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 150.0
Subtracting 0 from 5 leaves us with 5.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 44

Step 5:
44 can be fit into 59 1 times, resulting in a remainder of 15.
Write down 1 as next digit of the result. 
Result so far: 1501.0
If we subtract 44 from 59, we get 15.
Grab the next digit (7) from the dividend, add it to 15, then carry on: 157 / 44

Going ahead to step 6:
44 can be fit into 157 3 times, resulting in a remainder of 25.
Write down 3 as next digit of the result. 
Result so far: 15013.0
Subtract 132 from 157 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 7:
250 divided by 44 is 5 with a remainder of 30.
Record the quotient 5 as the next digit in the result. 
Result so far: 15013.5
Subtract 220 from 250 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 8:
When dividing 300 by 44, we get 6 with a remainder of 36.
Put 6 as the next digit of the answer. 
Result so far: 15013.56
If we take 264 away from 300, we end up 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.

Let's proceed to step 9:
The number 44 fits into 360 8 times, leaving a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 15013.568
If we subtract 352 from 360, 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.

On to step 10:
44 can be fit into 80 1 times, resulting in a remainder of 36.
The next digit of our result is 1. 
Result so far: 15013.5681
Subtract 44 from 80 to 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 11:
44 can be fit into 360 8 times, resulting in a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 15013.56818
Deduct 352 from 360 and we're left with 8.
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:
The number 44 fits into 80 1 times, leaving a remainder of 36.
Use 1 as the next digit of our solution. 
Result so far: 15013.568181
If we subtract 44 from 80, 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.

Step 13:
360 divided by 44 is 8 with a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 15013.5681818
If we take 352 away from 360, we end up with 8.
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 14:
If we divide 80 by 44, we get 1 and a remainder of 36.
Use 1 as the next digit of our solution. 
Result so far: 15013.56818181
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.

In conclusion, the division gives 15013.56818181 with a balance of 3.6e-08.