565663 ÷ 21 
The aim is to understand the frequency of 21 in 565663.

Step 1:
When dividing 5 by 21, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 21

Let's proceed to step 2:
56 divided by 21 is 2 with a remainder of 14.
Use 2 as the next digit of our solution. 
Result so far: 2.0
The remainder is 14 after subtracting 42 from 56.
Grab the next digit (5) from the dividend, add it to 14, then carry on: 145 / 21

Let's proceed to step 3:
21 can be fit into 145 6 times, resulting in a remainder of 19.
Use 6 as the next digit of our solution. 
Result so far: 26.0
Subtract 126 from 145 to get 19.
Grab the next digit (6) from the dividend, add it to 19, then carry on: 196 / 21

Advancing to step 4:
21 can be fit into 196 9 times, resulting in a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 269.0
Subtracting 189 from 196 leaves us with 7.
Append the next digit (6) from the dividend to 7 and continue with: 76 / 21

Advancing to step 5:
When dividing 76 by 21, we get 3 with a remainder of 13.
Put 3 as the next digit of the answer. 
Result so far: 2693.0
The remainder is 13 after subtracting 63 from 76.
Grab the next digit (3) from the dividend, add it to 13, then carry on: 133 / 21

On to step 6:
21 can be fit into 133 6 times, resulting in a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 26936.0
If we take 126 away from 133, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
70 divided by 21 is 3 with a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 26936.3
The remainder is 7 after subtracting 63 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 8:
The number 21 fits into 70 3 times, leaving a remainder of 7.
The next digit of our result is 3. 
Result so far: 26936.33
Deduct 63 from 70 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

After the division, we end up with 26936.33 and a remainder of 0.007.