We're dividing 437901 by 9 
We're looking to find how many times 9 goes into 437901.

Advancing to step 1:
If we divide 4 by 9, we get 0 and a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 9

Going ahead to step 2:
The number 9 fits into 43 4 times, leaving a remainder of 7.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtract 36 from 43 to get 7.
Take the next digit (7) from the dividend and append it to 7, then repeat: 77 / 9

Let's proceed to step 3:
When dividing 77 by 9, we get 8 with a remainder of 5.
Put 8 as the next digit of the answer. 
Result so far: 48.0
The remainder is 5 after subtracting 72 from 77.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 9

Step 4:
The number 9 fits into 59 6 times, leaving a remainder of 5.
The next digit of our result is 6. 
Result so far: 486.0
Subtract 54 from 59 to get 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 9

Step 5:
If we divide 50 by 9, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 4865.0
The remainder is 5 after subtracting 45 from 50.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 9

Advancing to step 6:
51 divided by 9 is 5 with a remainder of 6.
The next digit of our result is 5. 
Result so far: 48655.0
If we subtract 45 from 51, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 7:
60 divided by 9 is 6 with a remainder of 6.
The next digit of our result is 6. 
Result so far: 48655.6
Deduct 54 from 60 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 8:
The number 9 fits into 60 6 times, leaving a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 48655.66
The remainder is 6 after subtracting 54 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The quotient of the division is 48655.66, and the remainder is 0.006.