We look at the division of 781369 by 3 
We're looking to find how many times 3 goes into 781369.

Let's proceed to step 1:
3 can be fit into 7 2 times, resulting in a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtract 6 from 7 to get 1.
Append the next digit (8) from the dividend to 1 and continue with: 18 / 3

Step 2:
When dividing 18 by 3, we get 6 with a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 26.0
Subtract 18 from 18 to get 0.
Include the next digit (1) from the dividend after 0, then repeat: 1 / 3

Advancing to step 3:
1 divided by 3 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 260.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 3

Moving on to step 4:
3 goes into 13 4 times with a remainder of 1.
Record the quotient 4 as the next digit in the result. 
Result so far: 2604.0
If we take 12 away from 13, we end up with 1.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 3

Moving on to step 5:
3 can be fit into 16 5 times, resulting in a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 26045.0
If we subtract 15 from 16, we get 1.
Take the next digit (9) from the dividend and append it to 1, then repeat: 19 / 3

On to step 6:
3 can be fit into 19 6 times, resulting in a remainder of 1.
The next digit of our result is 6. 
Result so far: 260456.0
Subtract 18 from 19 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:
When dividing 10 by 3, we get 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 260456.3
Deduct 9 from 10 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.

Step 8:
When dividing 10 by 3, we get 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 260456.33
If we take 9 away from 10, we end up 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.

After the division, we end up with 260456.33 and a remainder of 0.001.