Let's divide 407666 by 75
Our goal is to divide 407666 by 75.

On to step 1:
4 divided by 75 is 0 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.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 75

On to step 2:
75 can be fit into 40 0 times, resulting in a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 40, we end up with 40.
Include the next digit (7) from the dividend after 40, then repeat: 407 / 75

Step 3:
75 can be fit into 407 5 times, resulting in a remainder of 32.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Subtract 375 from 407 to get 32.
Fetch the next digit (6) from the dividend, attach it to 32 and continue: 326 / 75

Moving on to step 4:
75 can be fit into 326 4 times, resulting in a remainder of 26.
The number 4 becomes the next digit in our result. 
Result so far: 54.0
Subtracting 300 from 326 leaves us with 26.
Include the next digit (6) from the dividend after 26, then repeat: 266 / 75

Advancing to step 5:
When dividing 266 by 75, we get 3 with a remainder of 41.
The number 3 becomes the next digit in our result. 
Result so far: 543.0
Subtract 225 from 266 to get 41.
Append the next digit (6) from the dividend to 41 and continue with: 416 / 75

Let's proceed to step 6:
416 divided by 75 is 5 with a remainder of 41.
Record the quotient 5 as the next digit in the result. 
Result so far: 5435.0
If we take 375 away from 416, we end up with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Let's proceed to step 7:
If we divide 410 by 75, we get 5 and a remainder of 35.
Write down 5 as next digit of the result. 
Result so far: 5435.5
If we take 375 away from 410, we end up 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.

Step 8:
75 goes into 350 4 times with a remainder of 50.
The next digit of our result is 4. 
Result so far: 5435.54
If we subtract 300 from 350, 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.

Advancing to step 9:
When dividing 500 by 75, we get 6 with a remainder of 50.
Write down 6 as next digit of the result. 
Result so far: 5435.546
If we take 450 away from 500, we end up 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.

Going ahead to step 10:
500 divided by 75 is 6 with a remainder of 50.
The next digit of our result is 6. 
Result so far: 5435.5466
Deduct 450 from 500 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.

The final result is 5435.5466 with a remainder of 0.0005.