712517 ÷ 75 
We want to figure out the number of times 712517 can be divided by 75.

Advancing to step 1:
If we divide 7 by 75, we get 0 and a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Include the next digit (1) from the dividend after 7, then repeat: 71 / 75

On to step 2:
The number 75 fits into 71 0 times, leaving a remainder of 71.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 71 to get 71.
Append the next digit (2) from the dividend to 71 and continue with: 712 / 75

On to step 3:
75 goes into 712 9 times with a remainder of 37.
Write down 9 as next digit of the result. 
Result so far: 9.0
If we take 675 away from 712, we end up with 37.
Grab the next digit (5) from the dividend, add it to 37, then carry on: 375 / 75

Let's proceed to step 4:
The number 75 fits into 375 5 times, leaving a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 95.0
Deduct 375 from 375 and we're left with 0.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 75

Going ahead to step 5:
75 goes into 1 0 times with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 950.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 75

Going ahead to step 6:
When dividing 17 by 75, we get 0 with a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 9500.0
If we take 0 away from 17, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 7:
75 can be fit into 170 2 times, resulting in a remainder of 20.
Write down 2 as next digit of the result. 
Result so far: 9500.2
Subtract 150 from 170 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.

Advancing to step 8:
If we divide 200 by 75, we get 2 and a remainder of 50.
Record the quotient 2 as the next digit in the result. 
Result so far: 9500.22
If we subtract 150 from 200, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The quotient of the division is 9500.22, and the remainder is 0.05.