We look at the division of 766688 by 44 
We're looking to find how many times 44 goes into 766688.

Going ahead to step 1:
If we divide 7 by 44, we get 0 and a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 44

Advancing to step 2:
76 divided by 44 is 1 with a remainder of 32.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 44 from 76, we get 32.
Append the next digit (6) from the dividend to 32 and continue with: 326 / 44

On to step 3:
If we divide 326 by 44, we get 7 and a remainder of 18.
The next digit of our result is 7. 
Result so far: 17.0
If we subtract 308 from 326, we get 18.
Bring next digit (6) of the dividend behind the 18 and repeat the process: 186 / 44

On to step 4:
If we divide 186 by 44, we get 4 and a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 174.0
If we take 176 away from 186, we end up with 10.
Take the next digit (8) from the dividend and append it to 10, then repeat: 108 / 44

Step 5:
When dividing 108 by 44, we get 2 with a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 1742.0
Deduct 88 from 108 and we're left with 20.
Include the next digit (8) from the dividend after 20, then repeat: 208 / 44

Moving on to step 6:
44 can be fit into 208 4 times, resulting in a remainder of 32.
The next digit of our result is 4. 
Result so far: 17424.0
The remainder is 32 after subtracting 176 from 208.
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 7:
The number 44 fits into 320 7 times, leaving a remainder of 12.
Put 7 as the next digit of the answer. 
Result so far: 17424.7
If we take 308 away from 320, we end up 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.

Going ahead to step 8:
The number 44 fits into 120 2 times, leaving a remainder of 32.
Use 2 as the next digit of our solution. 
Result so far: 17424.72
If we subtract 88 from 120, 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.

Going ahead to step 9:
44 can be fit into 320 7 times, resulting in a remainder of 12.
The next digit of our result is 7. 
Result so far: 17424.727
If we take 308 away from 320, we end up 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.

Step 10:
120 divided by 44 is 2 with a remainder of 32.
Record the quotient 2 as the next digit in the result. 
Result so far: 17424.7272
Deduct 88 from 120 and we're left 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.

On to step 11:
The number 44 fits into 320 7 times, leaving a remainder of 12.
Write down 7 as next digit of the result. 
Result so far: 17424.72727
The remainder is 12 after subtracting 308 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 12:
The number 44 fits into 120 2 times, leaving a remainder of 32.
The number 2 becomes the next digit in our result. 
Result so far: 17424.727272
If we subtract 88 from 120, 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.

Let's proceed to step 13:
When dividing 320 by 44, we get 7 with a remainder of 12.
Record the quotient 7 as the next digit in the result. 
Result so far: 17424.7272727
If we take 308 away from 320, we end up 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.

Moving on to step 14:
The number 44 fits into 120 2 times, leaving a remainder of 32.
The next digit of our result is 2. 
Result so far: 17424.72727272
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 final result is 17424.72727272 with a remainder of 3.2e-08.