17643 ÷ 77 
The aim is to understand the frequency of 77 in 17643.

Advancing to step 1:
If we divide 1 by 77, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 77

Let's proceed to step 2:
17 divided by 77 is 0 with a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Bring next digit (6) of the dividend behind the 17 and repeat the process: 176 / 77

Going ahead to step 3:
176 divided by 77 is 2 with a remainder of 22.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Deduct 154 from 176 and we're left with 22.
Append the next digit (4) from the dividend to 22 and continue with: 224 / 77

Let's proceed to step 4:
If we divide 224 by 77, we get 2 and a remainder of 70.
Write down 2 as next digit of the result. 
Result so far: 22.0
If we take 154 away from 224, we end up with 70.
Include the next digit (3) from the dividend after 70, then repeat: 703 / 77

Going ahead to step 5:
77 can be fit into 703 9 times, resulting in a remainder of 10.
Write down 9 as next digit of the result. 
Result so far: 229.0
If we take 693 away from 703, we end up 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 6:
When dividing 100 by 77, we get 1 with a remainder of 23.
The next digit of our result is 1. 
Result so far: 229.1
Subtracting 77 from 100 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 7:
77 goes into 230 2 times with a remainder of 76.
The next digit of our result is 2. 
Result so far: 229.12
Subtract 154 from 230 to get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Advancing to step 8:
77 goes into 760 9 times with a remainder of 67.
Write down 9 as next digit of the result. 
Result so far: 229.129
Subtracting 693 from 760 leaves us with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Step 9:
If we divide 670 by 77, we get 8 and a remainder of 54.
Write down 8 as next digit of the result. 
Result so far: 229.1298
If we subtract 616 from 670, we get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Advancing to step 10:
When dividing 540 by 77, we get 7 with a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 229.12987
Subtracting 539 from 540 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.

Advancing to step 11:
77 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 229.12987
Deduct 0 from 10 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.

Going ahead to step 12:
The number 77 fits into 100 1 times, leaving a remainder of 23.
Put 1 as the next digit of the answer. 
Result so far: 229.1298701
If we subtract 77 from 100, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 13:
The number 77 fits into 230 2 times, leaving a remainder of 76.
Put 2 as the next digit of the answer. 
Result so far: 229.12987012
The remainder is 76 after subtracting 154 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

The final outcome is 229.12987012, with a leftover of 7.6e-08.