We look at the division of 71665 by 41 
Our goal is to divide 71665 by 41.

Step 1:
7 divided by 41 is 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Fetch the next digit (1) from the dividend, attach it to 7 and continue: 71 / 41

On to step 2:
If we divide 71 by 41, we get 1 and a remainder of 30.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 41 from 71 and we're left with 30.
Fetch the next digit (6) from the dividend, attach it to 30 and continue: 306 / 41

Step 3:
If we divide 306 by 41, we get 7 and a remainder of 19.
Use 7 as the next digit of our solution. 
Result so far: 17.0
If we take 287 away from 306, we end up with 19.
Bring next digit (6) of the dividend behind the 19 and repeat the process: 196 / 41

On to step 4:
196 divided by 41 is 4 with a remainder of 32.
Write down 4 as next digit of the result. 
Result so far: 174.0
Deduct 164 from 196 and we're left with 32.
Bring next digit (5) of the dividend behind the 32 and repeat the process: 325 / 41

Let's proceed to step 5:
When dividing 325 by 41, we get 7 with a remainder of 38.
Use 7 as the next digit of our solution. 
Result so far: 1747.0
If we subtract 287 from 325, 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.

Moving on to step 6:
When dividing 380 by 41, we get 9 with a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 1747.9
The remainder is 11 after subtracting 369 from 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 7:
When dividing 110 by 41, we get 2 with a remainder of 28.
Use 2 as the next digit of our solution. 
Result so far: 1747.92
Subtracting 82 from 110 leaves us 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.

Going ahead to step 8:
41 goes into 280 6 times with a remainder of 34.
Write down 6 as next digit of the result. 
Result so far: 1747.926
If we take 246 away from 280, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 9:
41 goes into 340 8 times with a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 1747.9268
Subtracting 328 from 340 leaves us 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 10:
120 divided by 41 is 2 with a remainder of 38.
Write down 2 as next digit of the result. 
Result so far: 1747.92682
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.

Advancing to step 11:
41 goes into 380 9 times with a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 1747.926829
Deduct 369 from 380 and we're left 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.

On to step 12:
110 divided by 41 is 2 with a remainder of 28.
The number 2 becomes the next digit in our result. 
Result so far: 1747.9268292
Subtracting 82 from 110 leaves us 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.

Advancing to step 13:
When dividing 280 by 41, we get 6 with a remainder of 34.
Put 6 as the next digit of the answer. 
Result so far: 1747.92682926
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.

The final outcome is 1747.92682926, with a leftover of 3.4e-08.