We're dividing 430460 by 75 
We're looking to find how many times 75 goes into 430460.

Let's proceed to step 1:
75 goes into 4 0 times with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 75

Moving on to step 2:
43 divided by 75 is 0 with a remainder of 43.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 43 leaves us with 43.
Fetch the next digit (0) from the dividend, attach it to 43 and continue: 430 / 75

Advancing to step 3:
75 goes into 430 5 times with a remainder of 55.
The next digit of our result is 5. 
Result so far: 5.0
Deduct 375 from 430 and we're left with 55.
Take the next digit (4) from the dividend and append it to 55, then repeat: 554 / 75

Step 4:
75 goes into 554 7 times with a remainder of 29.
The number 7 becomes the next digit in our result. 
Result so far: 57.0
Deduct 525 from 554 and we're left with 29.
Grab the next digit (6) from the dividend, add it to 29, then carry on: 296 / 75

Step 5:
75 goes into 296 3 times with a remainder of 71.
Put 3 as the next digit of the answer. 
Result so far: 573.0
Subtract 225 from 296 to get 71.
Take the next digit (0) from the dividend and append it to 71, then repeat: 710 / 75

On to step 6:
The number 75 fits into 710 9 times, leaving a remainder of 35.
Use 9 as the next digit of our solution. 
Result so far: 5739.0
Subtracting 675 from 710 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 7:
350 divided by 75 is 4 with a remainder of 50.
The next digit of our result is 4. 
Result so far: 5739.4
Deduct 300 from 350 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 8:
500 divided by 75 is 6 with a remainder of 50.
The number 6 becomes the next digit in our result. 
Result so far: 5739.46
Subtracting 450 from 500 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 9:
When dividing 500 by 75, we get 6 with a remainder of 50.
Record the quotient 6 as the next digit in the result. 
Result so far: 5739.466
The remainder is 50 after subtracting 450 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final result is 5739.466 with a remainder of 0.005.