We're dividing 510590 by 65 
Our goal is to divide 510590 by 65.

Advancing to step 1:
The number 65 fits into 5 0 times, leaving a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 65

On to step 2:
The number 65 fits into 51 0 times, leaving a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Grab the next digit (0) from the dividend, add it to 51, then carry on: 510 / 65

Going ahead to step 3:
The number 65 fits into 510 7 times, leaving a remainder of 55.
Write down 7 as next digit of the result. 
Result so far: 7.0
Deduct 455 from 510 and we're left with 55.
Include the next digit (5) from the dividend after 55, then repeat: 555 / 65

On to step 4:
If we divide 555 by 65, we get 8 and a remainder of 35.
Record the quotient 8 as the next digit in the result. 
Result so far: 78.0
Subtracting 520 from 555 leaves us with 35.
Include the next digit (9) from the dividend after 35, then repeat: 359 / 65

Moving on to step 5:
When dividing 359 by 65, we get 5 with a remainder of 34.
Put 5 as the next digit of the answer. 
Result so far: 785.0
Subtract 325 from 359 to get 34.
Include the next digit (0) from the dividend after 34, then repeat: 340 / 65

Moving on to step 6:
The number 65 fits into 340 5 times, leaving a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 7855.0
Subtract 325 from 340 to 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 7:
65 can be fit into 150 2 times, resulting in a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 7855.2
If we subtract 130 from 150, we 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.

Going ahead to step 8:
65 goes into 200 3 times with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 7855.23
The remainder is 5 after subtracting 195 from 200.
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 9:
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: 7855.23
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 10:
65 goes into 500 7 times with a remainder of 45.
Record the quotient 7 as the next digit in the result. 
Result so far: 7855.2307
The remainder is 45 after subtracting 455 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 11:
65 goes into 450 6 times with a remainder of 60.
The number 6 becomes the next digit in our result. 
Result so far: 7855.23076
If we take 390 away from 450, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Moving on to step 12:
When dividing 600 by 65, we get 9 with a remainder of 15.
Put 9 as the next digit of the answer. 
Result so far: 7855.230769
If we take 585 away from 600, 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.

Going ahead to step 13:
When dividing 150 by 65, we get 2 with a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 7855.2307692
Deduct 130 from 150 and we're left 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.

Step 14:
65 goes into 200 3 times with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 7855.23076923
Subtract 195 from 200 to 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.

After the division, we end up with 7855.23076923 and a remainder of 5e-09.