We're dividing 85669 by 71 
The aim is to understand the frequency of 71 in 85669.

Step 1:
8 divided by 71 is 0 with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 71

Step 2:
When dividing 85 by 71, we get 1 with a remainder of 14.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 71 from 85 leaves us with 14.
Fetch the next digit (6) from the dividend, attach it to 14 and continue: 146 / 71

Let's proceed to step 3:
When dividing 146 by 71, we get 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
Subtracting 142 from 146 leaves us with 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 71

Moving on to step 4:
If we divide 46 by 71, we get 0 and a remainder of 46.
Use 0 as the next digit of our solution. 
Result so far: 120.0
If we take 0 away from 46, we end up with 46.
Append the next digit (9) from the dividend to 46 and continue with: 469 / 71

Step 5:
71 can be fit into 469 6 times, resulting in a remainder of 43.
The number 6 becomes the next digit in our result. 
Result so far: 1206.0
Subtracting 426 from 469 leaves us with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 6:
71 goes into 430 6 times with a remainder of 4.
The next digit of our result is 6. 
Result so far: 1206.6
Subtracting 426 from 430 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
The number 71 fits into 40 0 times, leaving a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 1206.6
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 8:
71 goes into 400 5 times with a remainder of 45.
The number 5 becomes the next digit in our result. 
Result so far: 1206.605
If we take 355 away from 400, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Let's proceed to step 9:
When dividing 450 by 71, we get 6 with a remainder of 24.
The next digit of our result is 6. 
Result so far: 1206.6056
The remainder is 24 after subtracting 426 from 450.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 10:
When dividing 240 by 71, we get 3 with a remainder of 27.
Record the quotient 3 as the next digit in the result. 
Result so far: 1206.60563
Subtract 213 from 240 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Moving on to step 11:
71 can be fit into 270 3 times, resulting in a remainder of 57.
Write down 3 as next digit of the result. 
Result so far: 1206.605633
Deduct 213 from 270 and we're left with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

The final result is 1206.605633 with a remainder of 5.7e-06.