507669 divided by 7 
The aim is to understand the frequency of 7 in 507669.

Going ahead to step 1:
5 divided by 7 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 7

Step 2:
When dividing 50 by 7, we get 7 with a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
If we subtract 49 from 50, we get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 7

Step 3:
If we divide 17 by 7, we get 2 and a remainder of 3.
Use 2 as the next digit of our solution. 
Result so far: 72.0
The remainder is 3 after subtracting 14 from 17.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 7

Going ahead to step 4:
The number 7 fits into 36 5 times, leaving a remainder of 1.
The next digit of our result is 5. 
Result so far: 725.0
Deduct 35 from 36 and we're left with 1.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 7

On to step 5:
7 can be fit into 16 2 times, resulting in a remainder of 2.
The next digit of our result is 2. 
Result so far: 7252.0
Subtract 14 from 16 to get 2.
Append the next digit (9) from the dividend to 2 and continue with: 29 / 7

Advancing to step 6:
When dividing 29 by 7, we get 4 with a remainder of 1.
The next digit of our result is 4. 
Result so far: 72524.0
Subtracting 28 from 29 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
When dividing 10 by 7, we get 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 72524.1
If we subtract 7 from 10, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 8:
30 divided by 7 is 4 with a remainder of 2.
The next digit of our result is 4. 
Result so far: 72524.14
If we take 28 away from 30, 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.

Step 9:
When dividing 20 by 7, we get 2 with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 72524.142
The remainder is 6 after subtracting 14 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 10:
If we divide 60 by 7, we get 8 and a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 72524.1428
The remainder is 4 after subtracting 56 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 11:
40 divided by 7 is 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 72524.14285
If we take 35 away from 40, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 12:
The number 7 fits into 50 7 times, leaving a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 72524.142857
If we subtract 49 from 50, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 13:
If we divide 10 by 7, we get 1 and a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 72524.1428571
Deduct 7 from 10 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 14:
When dividing 30 by 7, we get 4 with a remainder of 2.
Use 4 as the next digit of our solution. 
Result so far: 72524.14285714
Deduct 28 from 30 and we're left 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.

The final outcome is 72524.14285714, with a leftover of 2e-09.