We look at the division of 413005 by 65 
Our goal is to divide 413005 by 65.

Let's proceed to step 1:
4 divided by 65 is 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Fetch the next digit (1) from the dividend, attach it to 4 and continue: 41 / 65

Step 2:
The number 65 fits into 41 0 times, leaving a remainder of 41.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 41 after subtracting 0 from 41.
Fetch the next digit (3) from the dividend, attach it to 41 and continue: 413 / 65

Step 3:
The number 65 fits into 413 6 times, leaving a remainder of 23.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 390 from 413 and we're left with 23.
Take the next digit (0) from the dividend and append it to 23, then repeat: 230 / 65

Step 4:
65 goes into 230 3 times with a remainder of 35.
Write down 3 as next digit of the result. 
Result so far: 63.0
Deduct 195 from 230 and we're left with 35.
Take the next digit (0) from the dividend and append it to 35, then repeat: 350 / 65

On to step 5:
The number 65 fits into 350 5 times, leaving a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 635.0
If we subtract 325 from 350, we get 25.
Bring next digit (5) of the dividend behind the 25 and repeat the process: 255 / 65

Let's proceed to step 6:
If we divide 255 by 65, we get 3 and a remainder of 60.
Record the quotient 3 as the next digit in the result. 
Result so far: 6353.0
Subtract 195 from 255 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 7:
If we divide 600 by 65, we get 9 and a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 6353.9
Deduct 585 from 600 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
65 goes into 150 2 times with a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 6353.92
Subtracting 130 from 150 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 9:
When dividing 200 by 65, we get 3 with a remainder of 5.
Record the quotient 3 as the next digit in the result. 
Result so far: 6353.923
If we subtract 195 from 200, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 10:
65 can be fit into 50 0 times, resulting in a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 6353.923
Subtracting 0 from 50 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 11:
500 divided by 65 is 7 with a remainder of 45.
The number 7 becomes the next digit in our result. 
Result so far: 6353.92307
If we subtract 455 from 500, we get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 12:
65 can be fit into 450 6 times, resulting in a remainder of 60.
The number 6 becomes the next digit in our result. 
Result so far: 6353.923076
Subtract 390 from 450 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Going ahead to step 13:
If we divide 600 by 65, we get 9 and a remainder of 15.
Write down 9 as next digit of the result. 
Result so far: 6353.9230769
Deduct 585 from 600 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 14:
65 goes into 150 2 times with a remainder of 20.
Put 2 as the next digit of the answer. 
Result so far: 6353.92307692
Subtracting 130 from 150 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The quotient of the division is 6353.92307692, and the remainder is 2e-08.