257669 ÷ 19 
We want to figure out the number of times 257669 can be divided by 19.

Moving on to step 1:
The number 19 fits into 2 0 times, leaving a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 19

Let's proceed to step 2:
The number 19 fits into 25 1 times, leaving a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 19 from 25, we get 6.
Append the next digit (7) from the dividend to 6 and continue with: 67 / 19

Moving on to step 3:
When dividing 67 by 19, we get 3 with a remainder of 10.
The next digit of our result is 3. 
Result so far: 13.0
Subtracting 57 from 67 leaves us with 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 19

On to step 4:
106 divided by 19 is 5 with a remainder of 11.
The next digit of our result is 5. 
Result so far: 135.0
Deduct 95 from 106 and we're left with 11.
Append the next digit (6) from the dividend to 11 and continue with: 116 / 19

Let's proceed to step 5:
The number 19 fits into 116 6 times, leaving a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 1356.0
If we subtract 114 from 116, we get 2.
Fetch the next digit (9) from the dividend, attach it to 2 and continue: 29 / 19

Advancing to step 6:
29 divided by 19 is 1 with a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 13561.0
Subtract 19 from 29 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 7:
19 goes into 100 5 times with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 13561.5
If we take 95 away from 100, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
If we divide 50 by 19, we get 2 and a remainder of 12.
Use 2 as the next digit of our solution. 
Result so far: 13561.52
Deduct 38 from 50 and we're left 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.

Going ahead to step 9:
The number 19 fits into 120 6 times, leaving a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 13561.526
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.

Moving on to step 10:
60 divided by 19 is 3 with a remainder of 3.
The next digit of our result is 3. 
Result so far: 13561.5263
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.

On to step 11:
When dividing 30 by 19, we get 1 with a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 13561.52631
If we subtract 19 from 30, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 12:
19 goes into 110 5 times with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 13561.526315
The remainder is 15 after subtracting 95 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 13:
If we divide 150 by 19, we get 7 and a remainder of 17.
Put 7 as the next digit of the answer. 
Result so far: 13561.5263157
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.

Step 14:
If we divide 170 by 19, we get 8 and a remainder of 18.
Put 8 as the next digit of the answer. 
Result so far: 13561.52631578
If we subtract 152 from 170, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Our division results in 13561.52631578 with a remaining 1.8e-08.