We look at the division of 646601 by 44 
We're looking to find how many times 44 goes into 646601.

Going ahead to step 1:
6 divided by 44 is 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 44

Moving on to step 2:
The number 44 fits into 64 1 times, leaving a remainder of 20.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 44 from 64 and we're left with 20.
Include the next digit (6) from the dividend after 20, then repeat: 206 / 44

On to step 3:
44 goes into 206 4 times with a remainder of 30.
Write down 4 as next digit of the result. 
Result so far: 14.0
Subtracting 176 from 206 leaves us with 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 44

Let's proceed to step 4:
44 goes into 306 6 times with a remainder of 42.
The number 6 becomes the next digit in our result. 
Result so far: 146.0
If we take 264 away from 306, we end up with 42.
Append the next digit (0) from the dividend to 42 and continue with: 420 / 44

On to step 5:
420 divided by 44 is 9 with a remainder of 24.
The number 9 becomes the next digit in our result. 
Result so far: 1469.0
If we subtract 396 from 420, we get 24.
Grab the next digit (1) from the dividend, add it to 24, then carry on: 241 / 44

Step 6:
When dividing 241 by 44, we get 5 with a remainder of 21.
The next digit of our result is 5. 
Result so far: 14695.0
If we take 220 away from 241, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
210 divided by 44 is 4 with a remainder of 34.
Put 4 as the next digit of the answer. 
Result so far: 14695.4
Deduct 176 from 210 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.

Let's proceed to step 8:
The number 44 fits into 340 7 times, leaving a remainder of 32.
Put 7 as the next digit of the answer. 
Result so far: 14695.47
If we subtract 308 from 340, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 9:
The number 44 fits into 320 7 times, leaving a remainder of 12.
Record the quotient 7 as the next digit in the result. 
Result so far: 14695.477
Subtracting 308 from 320 leaves us 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.

The quotient of the division is 14695.477, and the remainder is 0.0012.