We're dividing 876266 by 13 
The aim is to understand the frequency of 13 in 876266.

Step 1:
The number 13 fits into 8 0 times, leaving a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Bring next digit (7) of the dividend behind the 8 and repeat the process: 87 / 13

On to step 2:
If we divide 87 by 13, we get 6 and a remainder of 9.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 78 from 87 and we're left with 9.
Take the next digit (6) from the dividend and append it to 9, then repeat: 96 / 13

Going ahead to step 3:
96 divided by 13 is 7 with a remainder of 5.
Record the quotient 7 as the next digit in the result. 
Result so far: 67.0
If we take 91 away from 96, we end up with 5.
Append the next digit (2) from the dividend to 5 and continue with: 52 / 13

Going ahead to step 4:
52 divided by 13 is 4 with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 674.0
If we take 52 away from 52, we end up with 0.
Fetch the next digit (6) from the dividend, attach it to 0 and continue: 6 / 13

On to step 5:
If we divide 6 by 13, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 6740.0
If we subtract 0 from 6, we get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 13

Advancing to step 6:
13 can be fit into 66 5 times, resulting in a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 67405.0
Subtract 65 from 66 to get 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:
10 divided by 13 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 67405.0
The remainder is 10 after subtracting 0 from 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 8:
If we divide 100 by 13, we get 7 and a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 67405.07
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 9:
When dividing 90 by 13, we get 6 with a remainder of 12.
The next digit of our result is 6. 
Result so far: 67405.076
Subtract 78 from 90 to 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.

Moving on to step 10:
When dividing 120 by 13, we get 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 67405.0769
Subtract 117 from 120 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 11:
If we divide 30 by 13, we get 2 and a remainder of 4.
The next digit of our result is 2. 
Result so far: 67405.07692
If we take 26 away from 30, we end up 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.

Advancing to step 12:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 67405.076923
Deduct 39 from 40 and we're left 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.

Let's proceed to step 13:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 67405.076923
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.

Advancing to step 14:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 67405.07692307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

After the division, we end up with 67405.07692307 and a remainder of 9e-09.