We look at the division of 421725 by 75 
Our goal is to divide 421725 by 75.

Advancing to step 1:
The number 75 fits into 4 0 times, leaving a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Include the next digit (2) from the dividend after 4, then repeat: 42 / 75

Going ahead to step 2:
The number 75 fits into 42 0 times, leaving a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 42 leaves us with 42.
Fetch the next digit (1) from the dividend, attach it to 42 and continue: 421 / 75

On to step 3:
The number 75 fits into 421 5 times, leaving a remainder of 46.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 375 away from 421, we end up with 46.
Bring next digit (7) of the dividend behind the 46 and repeat the process: 467 / 75

Going ahead to step 4:
467 divided by 75 is 6 with a remainder of 17.
The number 6 becomes the next digit in our result. 
Result so far: 56.0
Subtracting 450 from 467 leaves us with 17.
Take the next digit (2) from the dividend and append it to 17, then repeat: 172 / 75

Going ahead to step 5:
75 can be fit into 172 2 times, resulting in a remainder of 22.
Use 2 as the next digit of our solution. 
Result so far: 562.0
Deduct 150 from 172 and we're left with 22.
Grab the next digit (5) from the dividend, add it to 22, then carry on: 225 / 75

Step 6:
225 divided by 75 is 3 with a remainder of 0.
The next digit of our result is 3. 
Result so far: 5623.0
Deduct 225 from 225 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.

On to step 7:
0 divided by 75 is 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 5623.0
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 8:
If we divide 0 by 75, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 5623.0
Subtracting 0 from 0 leaves us 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 quotient of the division is 5623.0, and the remainder is 0.0.