654166 ÷ 19 
Our goal is to divide 654166 by 19.

Step 1:
If we divide 6 by 19, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (5) from the dividend after 6, then repeat: 65 / 19

Advancing to step 2:
When dividing 65 by 19, we get 3 with a remainder of 8.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
The remainder is 8 after subtracting 57 from 65.
Append the next digit (4) from the dividend to 8 and continue with: 84 / 19

Going ahead to step 3:
84 divided by 19 is 4 with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 34.0
If we take 76 away from 84, we end up with 8.
Grab the next digit (1) from the dividend, add it to 8, then carry on: 81 / 19

Moving on to step 4:
When dividing 81 by 19, we get 4 with a remainder of 5.
The next digit of our result is 4. 
Result so far: 344.0
The remainder is 5 after subtracting 76 from 81.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 19

Step 5:
19 can be fit into 56 2 times, resulting in a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 3442.0
Deduct 38 from 56 and we're left with 18.
Append the next digit (6) from the dividend to 18 and continue with: 186 / 19

Going ahead to step 6:
19 can be fit into 186 9 times, resulting in a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 34429.0
If we subtract 171 from 186, 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.

Advancing to step 7:
If we divide 150 by 19, we get 7 and a remainder of 17.
The next digit of our result is 7. 
Result so far: 34429.7
Subtracting 133 from 150 leaves us with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

On to step 8:
19 goes into 170 8 times with a remainder of 18.
The next digit of our result is 8. 
Result so far: 34429.78
Subtracting 152 from 170 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 9:
When dividing 180 by 19, we get 9 with a remainder of 9.
Record the quotient 9 as the next digit in the result. 
Result so far: 34429.789
Deduct 171 from 180 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 10:
90 divided by 19 is 4 with a remainder of 14.
The number 4 becomes the next digit in our result. 
Result so far: 34429.7894
Subtracting 76 from 90 leaves us 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 11:
The number 19 fits into 140 7 times, leaving a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 34429.78947
Subtracting 133 from 140 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 12:
When dividing 70 by 19, we get 3 with a remainder of 13.
Use 3 as the next digit of our solution. 
Result so far: 34429.789473
Deduct 57 from 70 and we're left 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.

Let's proceed to step 13:
The number 19 fits into 130 6 times, leaving a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 34429.7894736
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 14:
19 can be fit into 160 8 times, resulting in a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 34429.78947368
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.

Our division results in 34429.78947368 with a remaining 8e-09.