688584 ÷ 44 
Our goal is to divide 688584 by 44.

On to step 1:
44 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 44

On to step 2:
The number 44 fits into 68 1 times, leaving a remainder of 24.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 44 from 68, we get 24.
Fetch the next digit (8) from the dividend, attach it to 24 and continue: 248 / 44

Going ahead to step 3:
When dividing 248 by 44, we get 5 with a remainder of 28.
Use 5 as the next digit of our solution. 
Result so far: 15.0
If we subtract 220 from 248, we get 28.
Take the next digit (5) from the dividend and append it to 28, then repeat: 285 / 44

Step 4:
When dividing 285 by 44, we get 6 with a remainder of 21.
Put 6 as the next digit of the answer. 
Result so far: 156.0
If we subtract 264 from 285, we get 21.
Bring next digit (8) of the dividend behind the 21 and repeat the process: 218 / 44

Advancing to step 5:
When dividing 218 by 44, we get 4 with a remainder of 42.
The next digit of our result is 4. 
Result so far: 1564.0
The remainder is 42 after subtracting 176 from 218.
Append the next digit (4) from the dividend to 42 and continue with: 424 / 44

Moving on to step 6:
If we divide 424 by 44, we get 9 and a remainder of 28.
Write down 9 as next digit of the result. 
Result so far: 15649.0
If we take 396 away from 424, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 7:
44 goes into 280 6 times with a remainder of 16.
Put 6 as the next digit of the answer. 
Result so far: 15649.6
Subtract 264 from 280 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 8:
44 can be fit into 160 3 times, resulting in a remainder of 28.
Use 3 as the next digit of our solution. 
Result so far: 15649.63
The remainder is 28 after subtracting 132 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 9:
280 divided by 44 is 6 with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 15649.636
Subtract 264 from 280 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 10:
The number 44 fits into 160 3 times, leaving a remainder of 28.
Put 3 as the next digit of the answer. 
Result so far: 15649.6363
The remainder is 28 after subtracting 132 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 11:
44 can be fit into 280 6 times, resulting in a remainder of 16.
The next digit of our result is 6. 
Result so far: 15649.63636
Subtracting 264 from 280 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 12:
160 divided by 44 is 3 with a remainder of 28.
The next digit of our result is 3. 
Result so far: 15649.636363
If we take 132 away from 160, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 13:
44 goes into 280 6 times with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 15649.6363636
If we subtract 264 from 280, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 14:
160 divided by 44 is 3 with a remainder of 28.
The number 3 becomes the next digit in our result. 
Result so far: 15649.63636363
The remainder is 28 after subtracting 132 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

After the division, we end up with 15649.63636363 and a remainder of 2.8e-08.