We look at the division of 314034 by 19 
We're looking to find how many times 19 goes into 314034.

Step 1:
19 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 19

Moving on to step 2:
31 divided by 19 is 1 with a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 19 from 31 leaves us with 12.
Grab the next digit (4) from the dividend, add it to 12, then carry on: 124 / 19

On to step 3:
If we divide 124 by 19, we get 6 and a remainder of 10.
The next digit of our result is 6. 
Result so far: 16.0
If we subtract 114 from 124, we get 10.
Bring next digit (0) of the dividend behind the 10 and repeat the process: 100 / 19

On to step 4:
100 divided by 19 is 5 with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 165.0
If we subtract 95 from 100, we get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 19

Moving on to step 5:
When dividing 53 by 19, we get 2 with a remainder of 15.
Record the quotient 2 as the next digit in the result. 
Result so far: 1652.0
Subtract 38 from 53 to get 15.
Append the next digit (4) from the dividend to 15 and continue with: 154 / 19

On to step 6:
19 goes into 154 8 times with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 16528.0
Subtracting 152 from 154 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.

Step 7:
If we divide 20 by 19, we get 1 and a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 16528.1
Subtracting 19 from 20 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.

Advancing to step 8:
If we divide 10 by 19, we get 0 and a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 16528.1
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
19 can be fit into 100 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 16528.105
Subtract 95 from 100 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 10:
When dividing 50 by 19, we get 2 with a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 16528.1052
Subtract 38 from 50 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 11:
19 can be fit into 120 6 times, resulting in a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 16528.10526
Subtracting 114 from 120 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 12:
19 goes into 60 3 times with a remainder of 3.
The next digit of our result is 3. 
Result so far: 16528.105263
If we take 57 away from 60, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 13:
If we divide 30 by 19, we get 1 and a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 16528.1052631
The remainder is 11 after subtracting 19 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 14:
19 goes into 110 5 times with a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 16528.10526315
If we subtract 95 from 110, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

The final outcome is 16528.10526315, with a leftover of 1.5e-08.