156819 ÷ 19 
We want to figure out the number of times 156819 can be divided by 19.

On to step 1:
19 goes into 1 0 times with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Grab the next digit (5) from the dividend, add it to 1, then carry on: 15 / 19

Moving on to step 2:
When dividing 15 by 19, we get 0 with a remainder of 15.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 15, we get 15.
Take the next digit (6) from the dividend and append it to 15, then repeat: 156 / 19

Step 3:
If we divide 156 by 19, we get 8 and a remainder of 4.
The next digit of our result is 8. 
Result so far: 8.0
If we subtract 152 from 156, we get 4.
Append the next digit (8) from the dividend to 4 and continue with: 48 / 19

Moving on to step 4:
The number 19 fits into 48 2 times, leaving a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 82.0
Deduct 38 from 48 and we're left with 10.
Take the next digit (1) from the dividend and append it to 10, then repeat: 101 / 19

Moving on to step 5:
19 can be fit into 101 5 times, resulting in a remainder of 6.
The number 5 becomes the next digit in our result. 
Result so far: 825.0
Subtract 95 from 101 to get 6.
Append the next digit (9) from the dividend to 6 and continue with: 69 / 19

Moving on to step 6:
19 goes into 69 3 times with a remainder of 12.
Put 3 as the next digit of the answer. 
Result so far: 8253.0
If we take 57 away from 69, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 7:
19 goes into 120 6 times with a remainder of 6.
The next digit of our result is 6. 
Result so far: 8253.6
Deduct 114 from 120 and we're left 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.

Moving on to step 8:
60 divided by 19 is 3 with a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 8253.63
If we subtract 57 from 60, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 9:
The number 19 fits into 30 1 times, leaving a remainder of 11.
Record the quotient 1 as the next digit in the result. 
Result so far: 8253.631
Subtracting 19 from 30 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 10:
If we divide 110 by 19, we get 5 and a remainder of 15.
The next digit of our result is 5. 
Result so far: 8253.6315
If we take 95 away from 110, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 11:
150 divided by 19 is 7 with a remainder of 17.
Put 7 as the next digit of the answer. 
Result so far: 8253.63157
If we subtract 133 from 150, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 12:
170 divided by 19 is 8 with a remainder of 18.
Record the quotient 8 as the next digit in the result. 
Result so far: 8253.631578
The remainder is 18 after subtracting 152 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 13:
19 can be fit into 180 9 times, resulting in a remainder of 9.
The number 9 becomes the next digit in our result. 
Result so far: 8253.6315789
The remainder is 9 after subtracting 171 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 14:
19 can be fit into 90 4 times, resulting in a remainder of 14.
Put 4 as the next digit of the answer. 
Result so far: 8253.63157894
Subtract 76 from 90 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Our division results in 8253.63157894 with a remaining 1.4e-08.