We're dividing 81302567 by 3 
We're looking to find how many times 3 goes into 81302567.

Advancing to step 1:
When dividing 8 by 3, we get 2 with a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtract 6 from 8 to get 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 3

Step 2:
3 can be fit into 21 7 times, resulting in a remainder of 0.
Record the quotient 7 as the next digit in the result. 
Result so far: 27.0
If we subtract 21 from 21, we get 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 3

Let's proceed to step 3:
If we divide 3 by 3, we get 1 and a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 271.0
Subtracting 3 from 3 leaves us with 0.
Take the next digit (0) from the dividend and append it to 0, then repeat: 0 / 3

Advancing to step 4:
3 goes into 0 0 times with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 2710.0
Subtract 0 from 0 to get 0.
Include the next digit (2) from the dividend after 0, then repeat: 2 / 3

On to step 5:
3 goes into 2 0 times with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 27100.0
The remainder is 2 after subtracting 0 from 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 3

Going ahead to step 6:
The number 3 fits into 25 8 times, leaving a remainder of 1.
The next digit of our result is 8. 
Result so far: 271008.0
Subtracting 24 from 25 leaves us with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 3

On to step 7:
If we divide 16 by 3, we get 5 and a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 2710085.0
Subtracting 15 from 16 leaves us with 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 3

Let's proceed to step 8:
When dividing 17 by 3, we get 5 with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 27100855.0
Deduct 15 from 17 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 9:
If we divide 20 by 3, we get 6 and a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 27100855.6
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 10:
3 can be fit into 20 6 times, resulting in a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 27100855.66
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Our division results in 27100855.66 with a remaining 0.002.