We're dividing 513825 by 78 
We're looking to find how many times 78 goes into 513825.

Step 1:
78 can be fit into 5 0 times, resulting in a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 78

Let's proceed to step 2:
51 divided by 78 is 0 with a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Include the next digit (3) from the dividend after 51, then repeat: 513 / 78

Step 3:
78 can be fit into 513 6 times, resulting in a remainder of 45.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Deduct 468 from 513 and we're left with 45.
Append the next digit (8) from the dividend to 45 and continue with: 458 / 78

Step 4:
If we divide 458 by 78, we get 5 and a remainder of 68.
Put 5 as the next digit of the answer. 
Result so far: 65.0
Deduct 390 from 458 and we're left with 68.
Include the next digit (2) from the dividend after 68, then repeat: 682 / 78

On to step 5:
78 goes into 682 8 times with a remainder of 58.
Record the quotient 8 as the next digit in the result. 
Result so far: 658.0
If we take 624 away from 682, we end up with 58.
Grab the next digit (5) from the dividend, add it to 58, then carry on: 585 / 78

Advancing to step 6:
When dividing 585 by 78, we get 7 with a remainder of 39.
Write down 7 as next digit of the result. 
Result so far: 6587.0
The remainder is 39 after subtracting 546 from 585.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Advancing to step 7:
If we divide 390 by 78, we get 5 and a remainder of 0.
The next digit of our result is 5. 
Result so far: 6587.5
Deduct 390 from 390 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
When dividing 0 by 78, we get 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 6587.5
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 9:
0 divided by 78 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 6587.5
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 6587.5, with a leftover of 0.0.