431006 divided by 4 
The aim is to understand the frequency of 4 in 431006.

Going ahead to step 1:
If we divide 4 by 4, we get 1 and a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 0 after subtracting 4 from 4.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 4

Step 2:
The number 4 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 10.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (1) from the dividend and append it to 3, then repeat: 31 / 4

Going ahead to step 3:
When dividing 31 by 4, we get 7 with a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 107.0
Subtract 28 from 31 to get 3.
Fetch the next digit (0) from the dividend, attach it to 3 and continue: 30 / 4

On to step 4:
4 can be fit into 30 7 times, resulting in a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 1077.0
The remainder is 2 after subtracting 28 from 30.
Append the next digit (0) from the dividend to 2 and continue with: 20 / 4

Advancing to step 5:
4 goes into 20 5 times with a remainder of 0.
The next digit of our result is 5. 
Result so far: 10775.0
If we take 20 away from 20, we end up with 0.
Include the next digit (6) from the dividend after 0, then repeat: 6 / 4

Step 6:
4 can be fit into 6 1 times, resulting in a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 107751.0
The remainder is 2 after subtracting 4 from 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 7:
20 divided by 4 is 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 107751.5
If we subtract 20 from 20, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
4 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 107751.5
If we take 0 away from 0, we end up 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.

Moving on to step 9:
4 goes into 0 0 times with a remainder of 0.
The next digit of our result is 0. 
Result so far: 107751.5
Subtract 0 from 0 to get 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 107751.5, and the remainder is 0.0.