677566 divided by 43 
Our goal is to divide 677566 by 43.

On to step 1:
When dividing 6 by 43, we get 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 43

Going ahead to step 2:
When dividing 67 by 43, we get 1 with a remainder of 24.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 43 from 67 and we're left with 24.
Take the next digit (7) from the dividend and append it to 24, then repeat: 247 / 43

Let's proceed to step 3:
The number 43 fits into 247 5 times, leaving a remainder of 32.
The next digit of our result is 5. 
Result so far: 15.0
If we take 215 away from 247, we end up with 32.
Fetch the next digit (5) from the dividend, attach it to 32 and continue: 325 / 43

Let's proceed to step 4:
When dividing 325 by 43, we get 7 with a remainder of 24.
Write down 7 as next digit of the result. 
Result so far: 157.0
Subtracting 301 from 325 leaves us with 24.
Fetch the next digit (6) from the dividend, attach it to 24 and continue: 246 / 43

On to step 5:
If we divide 246 by 43, we get 5 and a remainder of 31.
Put 5 as the next digit of the answer. 
Result so far: 1575.0
The remainder is 31 after subtracting 215 from 246.
Grab the next digit (6) from the dividend, add it to 31, then carry on: 316 / 43

Step 6:
43 goes into 316 7 times with a remainder of 15.
Record the quotient 7 as the next digit in the result. 
Result so far: 15757.0
The remainder is 15 after subtracting 301 from 316.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 7:
The number 43 fits into 150 3 times, leaving a remainder of 21.
The number 3 becomes the next digit in our result. 
Result so far: 15757.3
If we subtract 129 from 150, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 8:
When dividing 210 by 43, we get 4 with a remainder of 38.
The number 4 becomes the next digit in our result. 
Result so far: 15757.34
If we subtract 172 from 210, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 9:
43 goes into 380 8 times with a remainder of 36.
Record the quotient 8 as the next digit in the result. 
Result so far: 15757.348
The remainder is 36 after subtracting 344 from 380.
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 10:
43 can be fit into 360 8 times, resulting in a remainder of 16.
The number 8 becomes the next digit in our result. 
Result so far: 15757.3488
If we subtract 344 from 360, 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.

The final result is 15757.3488 with a remainder of 0.00016.