We're dividing 681737 by 41 
We're looking to find how many times 41 goes into 681737.

Advancing to step 1:
If we divide 6 by 41, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (8) from the dividend after 6, then repeat: 68 / 41

Step 2:
41 can be fit into 68 1 times, resulting in a remainder of 27.
The next digit of our result is 1. 
Result so far: 1.0
If we take 41 away from 68, we end up with 27.
Grab the next digit (1) from the dividend, add it to 27, then carry on: 271 / 41

Let's proceed to step 3:
The number 41 fits into 271 6 times, leaving a remainder of 25.
Record the quotient 6 as the next digit in the result. 
Result so far: 16.0
Subtract 246 from 271 to get 25.
Bring next digit (7) of the dividend behind the 25 and repeat the process: 257 / 41

Moving on to step 4:
When dividing 257 by 41, we get 6 with a remainder of 11.
Put 6 as the next digit of the answer. 
Result so far: 166.0
If we subtract 246 from 257, we get 11.
Grab the next digit (3) from the dividend, add it to 11, then carry on: 113 / 41

Going ahead to step 5:
When dividing 113 by 41, we get 2 with a remainder of 31.
Record the quotient 2 as the next digit in the result. 
Result so far: 1662.0
If we take 82 away from 113, we end up with 31.
Fetch the next digit (7) from the dividend, attach it to 31 and continue: 317 / 41

On to step 6:
When dividing 317 by 41, we get 7 with a remainder of 30.
Record the quotient 7 as the next digit in the result. 
Result so far: 16627.0
If we subtract 287 from 317, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 7:
The number 41 fits into 300 7 times, leaving a remainder of 13.
The next digit of our result is 7. 
Result so far: 16627.7
The remainder is 13 after subtracting 287 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 8:
41 can be fit into 130 3 times, resulting in a remainder of 7.
The next digit of our result is 3. 
Result so far: 16627.73
If we take 123 away from 130, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 9:
The number 41 fits into 70 1 times, leaving a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 16627.731
Subtracting 41 from 70 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Step 10:
The number 41 fits into 290 7 times, leaving a remainder of 3.
The next digit of our result is 7. 
Result so far: 16627.7317
Subtracting 287 from 290 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 11:
41 can be fit into 30 0 times, resulting in a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 16627.7317
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 12:
When dividing 300 by 41, we get 7 with a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 16627.731707
Deduct 287 from 300 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 13:
41 goes into 130 3 times with a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 16627.7317073
Subtract 123 from 130 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 14:
When dividing 70 by 41, we get 1 with a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 16627.73170731
If we take 41 away from 70, we end up with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

The final outcome is 16627.73170731, with a leftover of 2.9e-08.