765009 ÷ 41 
Our goal is to divide 765009 by 41.

Going ahead to step 1:
When dividing 7 by 41, we get 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 41

Let's proceed to step 2:
If we divide 76 by 41, we get 1 and a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 35 after subtracting 41 from 76.
Append the next digit (5) from the dividend to 35 and continue with: 355 / 41

Let's proceed to step 3:
355 divided by 41 is 8 with a remainder of 27.
Use 8 as the next digit of our solution. 
Result so far: 18.0
Subtracting 328 from 355 leaves us with 27.
Grab the next digit (0) from the dividend, add it to 27, then carry on: 270 / 41

Let's proceed to step 4:
The number 41 fits into 270 6 times, leaving a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 186.0
The remainder is 24 after subtracting 246 from 270.
Fetch the next digit (0) from the dividend, attach it to 24 and continue: 240 / 41

Advancing to step 5:
When dividing 240 by 41, we get 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 1865.0
If we subtract 205 from 240, we get 35.
Include the next digit (9) from the dividend after 35, then repeat: 359 / 41

Step 6:
The number 41 fits into 359 8 times, leaving a remainder of 31.
Write down 8 as next digit of the result. 
Result so far: 18658.0
Subtract 328 from 359 to get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 7:
When dividing 310 by 41, we get 7 with a remainder of 23.
The next digit of our result is 7. 
Result so far: 18658.7
Subtract 287 from 310 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 8:
41 can be fit into 230 5 times, resulting in a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 18658.75
Deduct 205 from 230 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 9:
If we divide 250 by 41, we get 6 and a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 18658.756
Deduct 246 from 250 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 10:
The number 41 fits into 40 0 times, leaving a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 18658.756
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 11:
The number 41 fits into 400 9 times, leaving a remainder of 31.
Use 9 as the next digit of our solution. 
Result so far: 18658.75609
If we subtract 369 from 400, we get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Moving on to step 12:
41 goes into 310 7 times with a remainder of 23.
The number 7 becomes the next digit in our result. 
Result so far: 18658.756097
Subtract 287 from 310 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 13:
41 goes into 230 5 times with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 18658.7560975
The remainder is 25 after subtracting 205 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 14:
41 goes into 250 6 times with a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 18658.75609756
The remainder is 4 after subtracting 246 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final outcome is 18658.75609756, with a leftover of 4e-09.