Let's divide 517966 by 75
Our goal is to divide 517966 by 75.

Let's proceed to step 1:
75 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 75

On to step 2:
The number 75 fits into 51 0 times, leaving a remainder of 51.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Bring next digit (7) of the dividend behind the 51 and repeat the process: 517 / 75

Going ahead to step 3:
When dividing 517 by 75, we get 6 with a remainder of 67.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we take 450 away from 517, we end up with 67.
Take the next digit (9) from the dividend and append it to 67, then repeat: 679 / 75

On to step 4:
679 divided by 75 is 9 with a remainder of 4.
Record the quotient 9 as the next digit in the result. 
Result so far: 69.0
If we take 675 away from 679, we end up with 4.
Grab the next digit (6) from the dividend, add it to 4, then carry on: 46 / 75

Moving on to step 5:
When dividing 46 by 75, we get 0 with a remainder of 46.
The number 0 becomes the next digit in our result. 
Result so far: 690.0
The remainder is 46 after subtracting 0 from 46.
Bring next digit (6) of the dividend behind the 46 and repeat the process: 466 / 75

Moving on to step 6:
75 can be fit into 466 6 times, resulting in a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 6906.0
If we take 450 away from 466, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 7:
When dividing 160 by 75, we get 2 with a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 6906.2
The remainder is 10 after subtracting 150 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
100 divided by 75 is 1 with a remainder of 25.
Put 1 as the next digit of the answer. 
Result so far: 6906.21
Subtract 75 from 100 to 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.

Going ahead to step 9:
75 goes into 250 3 times with a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 6906.213
Subtract 225 from 250 to 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.

Step 10:
250 divided by 75 is 3 with a remainder of 25.
Use 3 as the next digit of our solution. 
Result so far: 6906.2133
Subtracting 225 from 250 leaves us 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 6906.2133, and the remainder is 0.00025.