677774 divided by 6 
The aim is to understand the frequency of 6 in 677774.

Moving on to step 1:
6 divided by 6 is 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 6 away from 6, we end up with 0.
Include the next digit (7) from the dividend after 0, then repeat: 7 / 6

Step 2:
7 divided by 6 is 1 with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 11.0
Subtracting 6 from 7 leaves us with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 6

Moving on to step 3:
17 divided by 6 is 2 with a remainder of 5.
Record the quotient 2 as the next digit in the result. 
Result so far: 112.0
If we take 12 away from 17, we end up with 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Moving on to step 4:
57 divided by 6 is 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 1129.0
Subtracting 54 from 57 leaves us with 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Let's proceed to step 5:
6 goes into 37 6 times with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 11296.0
If we subtract 36 from 37, we get 1.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 6

Let's proceed to step 6:
When dividing 14 by 6, we get 2 with a remainder of 2.
Put 2 as the next digit of the answer. 
Result so far: 112962.0
Subtracting 12 from 14 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
When dividing 20 by 6, we get 3 with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 112962.3
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
6 can be fit into 20 3 times, resulting in a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 112962.33
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 112962.33 and a remainder of 0.002.