We're dividing 289109 by 6 
The aim is to understand the frequency of 6 in 289109.

On to step 1:
2 divided by 6 is 0 with a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 6

Step 2:
6 can be fit into 28 4 times, resulting in a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 4.0
Deduct 24 from 28 and we're left with 4.
Append the next digit (9) from the dividend to 4 and continue with: 49 / 6

Let's proceed to step 3:
49 divided by 6 is 8 with a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 48.0
The remainder is 1 after subtracting 48 from 49.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 6

Let's proceed to step 4:
11 divided by 6 is 1 with a remainder of 5.
The number 1 becomes the next digit in our result. 
Result so far: 481.0
If we take 6 away from 11, we end up with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 6

Moving on to step 5:
6 goes into 50 8 times with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 4818.0
If we take 48 away from 50, we end up with 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 6

Advancing to step 6:
6 goes into 29 4 times with a remainder of 5.
The next digit of our result is 4. 
Result so far: 48184.0
If we subtract 24 from 29, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 7:
50 divided by 6 is 8 with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 48184.8
Subtract 48 from 50 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
If we divide 20 by 6, we get 3 and a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 48184.83
If we subtract 18 from 20, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 9:
If we divide 20 by 6, we get 3 and a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 48184.833
If we subtract 18 from 20, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 48184.833, and the remainder is 0.0002.