1661 ÷ 77 
The aim is to understand the frequency of 77 in 1661.

Going ahead to step 1:
The number 77 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 77

Moving on to step 2:
When dividing 16 by 77, we get 0 with a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 16 leaves us with 16.
Grab the next digit (6) from the dividend, add it to 16, then carry on: 166 / 77

Step 3:
The number 77 fits into 166 2 times, leaving a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 2.0
If we subtract 154 from 166, we get 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 77

Moving on to step 4:
When dividing 121 by 77, we get 1 with a remainder of 44.
The number 1 becomes the next digit in our result. 
Result so far: 21.0
If we take 77 away from 121, we end up with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Going ahead to step 5:
77 can be fit into 440 5 times, resulting in a remainder of 55.
The next digit of our result is 5. 
Result so far: 21.5
Subtract 385 from 440 to get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 6:
When dividing 550 by 77, we get 7 with a remainder of 11.
Use 7 as the next digit of our solution. 
Result so far: 21.57
Subtract 539 from 550 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 7:
If we divide 110 by 77, we get 1 and a remainder of 33.
The number 1 becomes the next digit in our result. 
Result so far: 21.571
If we subtract 77 from 110, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 8:
77 can be fit into 330 4 times, resulting in a remainder of 22.
The number 4 becomes the next digit in our result. 
Result so far: 21.5714
Subtracting 308 from 330 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 9:
When dividing 220 by 77, we get 2 with a remainder of 66.
The number 2 becomes the next digit in our result. 
Result so far: 21.57142
If we subtract 154 from 220, we get 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

On to step 10:
The number 77 fits into 660 8 times, leaving a remainder of 44.
Put 8 as the next digit of the answer. 
Result so far: 21.571428
If we take 616 away from 660, we end up with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 11:
The number 77 fits into 440 5 times, leaving a remainder of 55.
Record the quotient 5 as the next digit in the result. 
Result so far: 21.5714285
The remainder is 55 after subtracting 385 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 12:
77 can be fit into 550 7 times, resulting in a remainder of 11.
Use 7 as the next digit of our solution. 
Result so far: 21.57142857
The remainder is 11 after subtracting 539 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

After the division, we end up with 21.57142857 and a remainder of 1.1e-08.