We look at the division of 365984 by 65 
We want to figure out the number of times 365984 can be divided by 65.

Advancing to step 1:
The number 65 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 65

On to step 2:
If we divide 36 by 65, we get 0 and a remainder of 36.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 36 leaves us with 36.
Include the next digit (5) from the dividend after 36, then repeat: 365 / 65

On to step 3:
When dividing 365 by 65, we get 5 with a remainder of 40.
Write down 5 as next digit of the result. 
Result so far: 5.0
The remainder is 40 after subtracting 325 from 365.
Grab the next digit (9) from the dividend, add it to 40, then carry on: 409 / 65

On to step 4:
65 goes into 409 6 times with a remainder of 19.
Record the quotient 6 as the next digit in the result. 
Result so far: 56.0
Deduct 390 from 409 and we're left with 19.
Take the next digit (8) from the dividend and append it to 19, then repeat: 198 / 65

Moving on to step 5:
When dividing 198 by 65, we get 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 563.0
Deduct 195 from 198 and we're left with 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 65

Going ahead to step 6:
65 goes into 34 0 times with a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 5630.0
If we take 0 away from 34, 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.

Moving on to step 7:
When dividing 340 by 65, we get 5 with a remainder of 15.
The next digit of our result is 5. 
Result so far: 5630.5
If we take 325 away from 340, we end up 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.

On to step 8:
If we divide 150 by 65, we get 2 and a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 5630.52
Subtract 130 from 150 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 9:
If we divide 200 by 65, we get 3 and a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 5630.523
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.

Let's proceed to step 10:
The number 65 fits into 50 0 times, leaving a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 5630.523
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.

Let's proceed to step 11:
When dividing 500 by 65, we get 7 with a remainder of 45.
The number 7 becomes the next digit in our result. 
Result so far: 5630.52307
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.

Step 12:
450 divided by 65 is 6 with a remainder of 60.
Put 6 as the next digit of the answer. 
Result so far: 5630.523076
The remainder is 60 after subtracting 390 from 450.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 13:
65 goes into 600 9 times with a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 5630.5230769
If we subtract 585 from 600, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 14:
65 can be fit into 150 2 times, resulting in a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 5630.52307692
If we take 130 away from 150, we end up 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 final result is 5630.52307692 with a remainder of 2e-08.