We're dividing 940261 by 3 
We're looking to find how many times 3 goes into 940261.

Going ahead to step 1:
3 goes into 9 3 times with a remainder of 0.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtract 9 from 9 to get 0.
Fetch the next digit (4) from the dividend, attach it to 0 and continue: 4 / 3

Advancing to step 2:
The number 3 fits into 4 1 times, leaving a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 31.0
Subtract 3 from 4 to get 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 3

Going ahead to step 3:
3 goes into 10 3 times with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 313.0
If we subtract 9 from 10, we get 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 3

Moving on to step 4:
12 divided by 3 is 4 with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 3134.0
The remainder is 0 after subtracting 12 from 12.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 3

Step 5:
3 can be fit into 6 2 times, resulting in a remainder of 0.
The next digit of our result is 2. 
Result so far: 31342.0
If we subtract 6 from 6, we get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 3

Step 6:
When dividing 1 by 3, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 313420.0
The remainder is 1 after subtracting 0 from 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 7:
The number 3 fits into 10 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 313420.3
Subtracting 9 from 10 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.

Let's proceed to step 8:
10 divided by 3 is 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 313420.33
Subtract 9 from 10 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.

The quotient of the division is 313420.33, and the remainder is 0.001.