We divide 145974 by 19
Our goal is to divide 145974 by 19.

Advancing to step 1:
1 divided by 19 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 19

Moving on to step 2:
The number 19 fits into 14 0 times, leaving a remainder of 14.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 14, we get 14.
Append the next digit (5) from the dividend to 14 and continue with: 145 / 19

Going ahead to step 3:
The number 19 fits into 145 7 times, leaving a remainder of 12.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Subtracting 133 from 145 leaves us with 12.
Grab the next digit (9) from the dividend, add it to 12, then carry on: 129 / 19

Step 4:
129 divided by 19 is 6 with a remainder of 15.
Use 6 as the next digit of our solution. 
Result so far: 76.0
Subtracting 114 from 129 leaves us with 15.
Grab the next digit (7) from the dividend, add it to 15, then carry on: 157 / 19

Let's proceed to step 5:
The number 19 fits into 157 8 times, leaving a remainder of 5.
The next digit of our result is 8. 
Result so far: 768.0
If we take 152 away from 157, we end up with 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 19

Moving on to step 6:
If we divide 54 by 19, we get 2 and a remainder of 16.
The number 2 becomes the next digit in our result. 
Result so far: 7682.0
If we subtract 38 from 54, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 7:
160 divided by 19 is 8 with a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 7682.8
Deduct 152 from 160 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 8:
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: 7682.84
The remainder is 4 after subtracting 76 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
19 goes into 40 2 times with a remainder of 2.
The next digit of our result is 2. 
Result so far: 7682.842
If we take 38 away from 40, we end up 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.

On to step 10:
20 divided by 19 is 1 with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 7682.8421
The remainder is 1 after subtracting 19 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 11:
The number 19 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 7682.8421
Subtracting 0 from 10 leaves us 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.

Step 12:
If we divide 100 by 19, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 7682.842105
If we subtract 95 from 100, we 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.

Step 13:
19 goes into 50 2 times with a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 7682.8421052
The remainder is 12 after subtracting 38 from 50.
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 14:
19 goes into 120 6 times with a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 7682.84210526
If we take 114 away from 120, we end up 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.

The quotient of the division is 7682.84210526, and the remainder is 6e-09.