We're dividing 350659 by 44 
We're looking to find how many times 44 goes into 350659.

Moving on to step 1:
When dividing 3 by 44, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 44

Let's proceed to step 2:
If we divide 35 by 44, we get 0 and a remainder of 35.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 35 after subtracting 0 from 35.
Append the next digit (0) from the dividend to 35 and continue with: 350 / 44

Step 3:
If we divide 350 by 44, we get 7 and a remainder of 42.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
If we subtract 308 from 350, we get 42.
Take the next digit (6) from the dividend and append it to 42, then repeat: 426 / 44

On to step 4:
The number 44 fits into 426 9 times, leaving a remainder of 30.
Use 9 as the next digit of our solution. 
Result so far: 79.0
If we take 396 away from 426, we end up with 30.
Take the next digit (5) from the dividend and append it to 30, then repeat: 305 / 44

Going ahead to step 5:
44 goes into 305 6 times with a remainder of 41.
Write down 6 as next digit of the result. 
Result so far: 796.0
Deduct 264 from 305 and we're left with 41.
Take the next digit (9) from the dividend and append it to 41, then repeat: 419 / 44

Step 6:
If we divide 419 by 44, we get 9 and a remainder of 23.
The number 9 becomes the next digit in our result. 
Result so far: 7969.0
If we subtract 396 from 419, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 7:
44 can be fit into 230 5 times, resulting in a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 7969.5
Subtracting 220 from 230 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.

Let's proceed to step 8:
The number 44 fits into 100 2 times, leaving a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 7969.52
Deduct 88 from 100 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 9:
44 goes into 120 2 times with a remainder of 32.
Write down 2 as next digit of the result. 
Result so far: 7969.522
Subtracting 88 from 120 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The quotient of the division is 7969.522, and the remainder is 0.0032.