We divide 507778 by 75
Our goal is to divide 507778 by 75.

Step 1:
When dividing 5 by 75, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 75

Moving on to step 2:
75 goes into 50 0 times with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 50, we get 50.
Take the next digit (7) from the dividend and append it to 50, then repeat: 507 / 75

Going ahead to step 3:
507 divided by 75 is 6 with a remainder of 57.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 450 from 507, we get 57.
Grab the next digit (7) from the dividend, add it to 57, then carry on: 577 / 75

Let's proceed to step 4:
If we divide 577 by 75, we get 7 and a remainder of 52.
The number 7 becomes the next digit in our result. 
Result so far: 67.0
If we take 525 away from 577, we end up with 52.
Bring next digit (7) of the dividend behind the 52 and repeat the process: 527 / 75

Going ahead to step 5:
75 goes into 527 7 times with a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 677.0
If we take 525 away from 527, we end up with 2.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 75

Advancing to step 6:
If we divide 28 by 75, we get 0 and a remainder of 28.
Put 0 as the next digit of the answer. 
Result so far: 6770.0
Deduct 0 from 28 and we're left 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 7:
280 divided by 75 is 3 with a remainder of 55.
Write down 3 as next digit of the result. 
Result so far: 6770.3
The remainder is 55 after subtracting 225 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 8:
When dividing 550 by 75, we get 7 with a remainder of 25.
Write down 7 as next digit of the result. 
Result so far: 6770.37
If we subtract 525 from 550, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 9:
If we divide 250 by 75, we get 3 and a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 6770.373
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 10:
The number 75 fits into 250 3 times, leaving a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 6770.3733
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 6770.3733, and the remainder is 0.00025.