771717 ÷ 22 
The aim is to understand the frequency of 22 in 771717.

Step 1:
The number 22 fits into 7 0 times, leaving a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 22

Step 2:
If we divide 77 by 22, we get 3 and a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Deduct 66 from 77 and we're left with 11.
Append the next digit (1) from the dividend to 11 and continue with: 111 / 22

Advancing to step 3:
If we divide 111 by 22, we get 5 and a remainder of 1.
Record the quotient 5 as the next digit in the result. 
Result so far: 35.0
If we take 110 away from 111, we end up with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 22

On to step 4:
17 divided by 22 is 0 with a remainder of 17.
The next digit of our result is 0. 
Result so far: 350.0
Deduct 0 from 17 and we're left with 17.
Take the next digit (1) from the dividend and append it to 17, then repeat: 171 / 22

Let's proceed to step 5:
171 divided by 22 is 7 with a remainder of 17.
The number 7 becomes the next digit in our result. 
Result so far: 3507.0
The remainder is 17 after subtracting 154 from 171.
Bring next digit (7) of the dividend behind the 17 and repeat the process: 177 / 22

On to step 6:
22 goes into 177 8 times with a remainder of 1.
The number 8 becomes the next digit in our result. 
Result so far: 35078.0
If we take 176 away from 177, we end up 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:
The number 22 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 35078.0
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 8:
The number 22 fits into 100 4 times, leaving a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 35078.04
If we subtract 88 from 100, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 9:
120 divided by 22 is 5 with a remainder of 10.
The next digit of our result is 5. 
Result so far: 35078.045
Deduct 110 from 120 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 10:
22 can be fit into 100 4 times, resulting in a remainder of 12.
The next digit of our result is 4. 
Result so far: 35078.0454
Subtracting 88 from 100 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 11:
22 goes into 120 5 times with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 35078.04545
The remainder is 10 after subtracting 110 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 12:
When dividing 100 by 22, we get 4 with a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 35078.045454
Deduct 88 from 100 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 13:
22 can be fit into 120 5 times, resulting in a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 35078.0454545
Deduct 110 from 120 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 14:
The number 22 fits into 100 4 times, leaving a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 35078.04545454
Deduct 88 from 100 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

After the division, we end up with 35078.04545454 and a remainder of 1.2e-08.