677184 ÷ 41 
Let's see how many times 41 fits into 677184.

On to step 1:
When dividing 6 by 41, we get 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Append the next digit (7) from the dividend to 6 and continue with: 67 / 41

Going ahead to step 2:
67 divided by 41 is 1 with a remainder of 26.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 26 after subtracting 41 from 67.
Include the next digit (7) from the dividend after 26, then repeat: 267 / 41

Going ahead to step 3:
The number 41 fits into 267 6 times, leaving a remainder of 21.
Use 6 as the next digit of our solution. 
Result so far: 16.0
If we subtract 246 from 267, we get 21.
Append the next digit (1) from the dividend to 21 and continue with: 211 / 41

Going ahead to step 4:
When dividing 211 by 41, we get 5 with a remainder of 6.
Use 5 as the next digit of our solution. 
Result so far: 165.0
If we subtract 205 from 211, we get 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 41

Step 5:
41 can be fit into 68 1 times, resulting in a remainder of 27.
Record the quotient 1 as the next digit in the result. 
Result so far: 1651.0
Deduct 41 from 68 and we're left with 27.
Take the next digit (4) from the dividend and append it to 27, then repeat: 274 / 41

Advancing to step 6:
When dividing 274 by 41, we get 6 with a remainder of 28.
The number 6 becomes the next digit in our result. 
Result so far: 16516.0
Deduct 246 from 274 and we're left 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.

Step 7:
280 divided by 41 is 6 with a remainder of 34.
Record the quotient 6 as the next digit in the result. 
Result so far: 16516.6
If we subtract 246 from 280, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 8:
When dividing 340 by 41, we get 8 with a remainder of 12.
The next digit of our result is 8. 
Result so far: 16516.68
Deduct 328 from 340 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:
120 divided by 41 is 2 with a remainder of 38.
Record the quotient 2 as the next digit in the result. 
Result so far: 16516.682
Subtracting 82 from 120 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

On to step 10:
The number 41 fits into 380 9 times, leaving a remainder of 11.
The next digit of our result is 9. 
Result so far: 16516.6829
If we take 369 away from 380, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 11:
41 can be fit into 110 2 times, resulting in a remainder of 28.
Write down 2 as next digit of the result. 
Result so far: 16516.68292
The remainder is 28 after subtracting 82 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 12:
41 can be fit into 280 6 times, resulting in a remainder of 34.
Record the quotient 6 as the next digit in the result. 
Result so far: 16516.682926
If we subtract 246 from 280, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 13:
The number 41 fits into 340 8 times, leaving a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 16516.6829268
The remainder is 12 after subtracting 328 from 340.
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 14:
120 divided by 41 is 2 with a remainder of 38.
The number 2 becomes the next digit in our result. 
Result so far: 16516.68292682
If we subtract 82 from 120, 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.

After the division, we end up with 16516.68292682 and a remainder of 3.8e-08.