We're dividing 425669 by 75 
We want to figure out the number of times 425669 can be divided by 75.

Going ahead to step 1:
75 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 75

Let's proceed to step 2:
75 can be fit into 42 0 times, resulting in a remainder of 42.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 42 after subtracting 0 from 42.
Take the next digit (5) from the dividend and append it to 42, then repeat: 425 / 75

Moving on to step 3:
The number 75 fits into 425 5 times, leaving a remainder of 50.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
If we take 375 away from 425, we end up with 50.
Fetch the next digit (6) from the dividend, attach it to 50 and continue: 506 / 75

Let's proceed to step 4:
506 divided by 75 is 6 with a remainder of 56.
The next digit of our result is 6. 
Result so far: 56.0
If we subtract 450 from 506, we get 56.
Take the next digit (6) from the dividend and append it to 56, then repeat: 566 / 75

Let's proceed to step 5:
75 can be fit into 566 7 times, resulting in a remainder of 41.
Use 7 as the next digit of our solution. 
Result so far: 567.0
If we take 525 away from 566, we end up with 41.
Include the next digit (9) from the dividend after 41, then repeat: 419 / 75

Going ahead to step 6:
75 goes into 419 5 times with a remainder of 44.
The number 5 becomes the next digit in our result. 
Result so far: 5675.0
If we take 375 away from 419, we end up with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 7:
75 can be fit into 440 5 times, resulting in a remainder of 65.
Write down 5 as next digit of the result. 
Result so far: 5675.5
If we subtract 375 from 440, we get 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Let's proceed to step 8:
75 can be fit into 650 8 times, resulting in a remainder of 50.
The number 8 becomes the next digit in our result. 
Result so far: 5675.58
If we subtract 600 from 650, 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.

Moving on to step 9:
If we divide 500 by 75, we get 6 and a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 5675.586
Subtract 450 from 500 to 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.

On to step 10:
75 can be fit into 500 6 times, resulting in a remainder of 50.
The next digit of our result is 6. 
Result so far: 5675.5866
If we subtract 450 from 500, 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 5675.5866, and the remainder is 0.0005.