We look at the division of 42319 by 3 
We're looking to find how many times 3 goes into 42319.

On to step 1:
3 goes into 4 1 times with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 3 from 4 leaves us with 1.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 3

On to step 2:
12 divided by 3 is 4 with a remainder of 0.
Record the quotient 4 as the next digit in the result. 
Result so far: 14.0
If we take 12 away from 12, we end up with 0.
Fetch the next digit (3) from the dividend, attach it to 0 and continue: 3 / 3

On to step 3:
3 can be fit into 3 1 times, resulting in a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 141.0
If we subtract 3 from 3, we get 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 3

Advancing to step 4:
3 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 1410.0
Subtract 0 from 1 to get 1.
Append the next digit (9) from the dividend to 1 and continue with: 19 / 3

Going ahead to step 5:
3 goes into 19 6 times with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 14106.0
If we take 18 away from 19, 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.

Going ahead to step 6:
3 can be fit into 10 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 14106.3
The remainder is 1 after subtracting 9 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
3 goes into 10 3 times with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 14106.33
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.

In conclusion, the division gives 14106.33 with a balance of 0.001.