We look at the division of 345191 by 3 
We want to figure out the number of times 345191 can be divided by 3.

Advancing to step 1:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 3 away from 3, we end up with 0.
Append the next digit (4) from the dividend to 0 and continue with: 4 / 3

Going ahead to step 2:
If we divide 4 by 3, we get 1 and a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
Subtract 3 from 4 to get 1.
Grab the next digit (5) from the dividend, add it to 1, then carry on: 15 / 3

Step 3:
If we divide 15 by 3, we get 5 and a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 115.0
If we subtract 15 from 15, we get 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 3

Let's proceed to step 4:
1 divided by 3 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 1150.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (9) from the dividend, attach it to 1 and continue: 19 / 3

Advancing to step 5:
3 goes into 19 6 times with a remainder of 1.
The next digit of our result is 6. 
Result so far: 11506.0
Subtracting 18 from 19 leaves us with 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 3

Moving on to step 6:
3 can be fit into 11 3 times, resulting in a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 115063.0
If we take 9 away from 11, we end up 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.

On to step 7:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 115063.6
Subtracting 18 from 20 leaves us 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.

On to step 8:
If we divide 20 by 3, we get 6 and a remainder of 2.
The next digit of our result is 6. 
Result so far: 115063.66
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 115063.66 with a remaining 0.002.