We look at the division of 377164 by 19 
We want to divide 377164 by 19.

Step 1:
If we divide 3 by 19, we get 0 and a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 19

Moving on to step 2:
37 divided by 19 is 1 with a remainder of 18.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 19 from 37 leaves us with 18.
Take the next digit (7) from the dividend and append it to 18, then repeat: 187 / 19

Let's proceed to step 3:
The number 19 fits into 187 9 times, leaving a remainder of 16.
Put 9 as the next digit of the answer. 
Result so far: 19.0
The remainder is 16 after subtracting 171 from 187.
Bring next digit (1) of the dividend behind the 16 and repeat the process: 161 / 19

Going ahead to step 4:
19 can be fit into 161 8 times, resulting in a remainder of 9.
The next digit of our result is 8. 
Result so far: 198.0
The remainder is 9 after subtracting 152 from 161.
Append the next digit (6) from the dividend to 9 and continue with: 96 / 19

Going ahead to step 5:
The number 19 fits into 96 5 times, leaving a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 1985.0
If we subtract 95 from 96, we get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 19

Going ahead to step 6:
When dividing 14 by 19, we get 0 with a remainder of 14.
The next digit of our result is 0. 
Result so far: 19850.0
Deduct 0 from 14 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
19 can be fit into 140 7 times, resulting in a remainder of 7.
Write down 7 as next digit of the result. 
Result so far: 19850.7
If we subtract 133 from 140, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 8:
When dividing 70 by 19, we get 3 with a remainder of 13.
The number 3 becomes the next digit in our result. 
Result so far: 19850.73
If we take 57 away from 70, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 9:
When dividing 130 by 19, we get 6 with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 19850.736
Deduct 114 from 130 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 10:
160 divided by 19 is 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 19850.7368
If we subtract 152 from 160, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 11:
19 can be fit into 80 4 times, resulting in a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 19850.73684
Subtract 76 from 80 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 12:
40 divided by 19 is 2 with a remainder of 2.
Put 2 as the next digit of the answer. 
Result so far: 19850.736842
If we subtract 38 from 40, we 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.

Step 13:
When dividing 20 by 19, we get 1 with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 19850.7368421
If we subtract 19 from 20, we 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.

Let's proceed to step 14:
19 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 19850.7368421
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.

The quotient of the division is 19850.7368421, and the remainder is 1e-08.