We're dividing 129674 by 19 
We're looking to find how many times 19 goes into 129674.

On to step 1:
1 divided by 19 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 19

Moving on to step 2:
12 divided by 19 is 0 with a remainder of 12.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 12, we get 12.
Fetch the next digit (9) from the dividend, attach it to 12 and continue: 129 / 19

Let's proceed to step 3:
19 goes into 129 6 times with a remainder of 15.
Write down 6 as next digit of the result. 
Result so far: 6.0
Subtracting 114 from 129 leaves us with 15.
Bring next digit (6) of the dividend behind the 15 and repeat the process: 156 / 19

Step 4:
19 goes into 156 8 times with a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 68.0
If we subtract 152 from 156, we get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 19

On to step 5:
19 can be fit into 47 2 times, resulting in a remainder of 9.
Write down 2 as next digit of the result. 
Result so far: 682.0
Deduct 38 from 47 and we're left with 9.
Fetch the next digit (4) from the dividend, attach it to 9 and continue: 94 / 19

Let's proceed to step 6:
If we divide 94 by 19, we get 4 and a remainder of 18.
Record the quotient 4 as the next digit in the result. 
Result so far: 6824.0
Subtract 76 from 94 to 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.

Going ahead to step 7:
180 divided by 19 is 9 with a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 6824.9
Subtract 171 from 180 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 8:
19 goes into 90 4 times with a remainder of 14.
Record the quotient 4 as the next digit in the result. 
Result so far: 6824.94
Deduct 76 from 90 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.

Step 9:
19 goes into 140 7 times with a remainder of 7.
Write down 7 as next digit of the result. 
Result so far: 6824.947
If we take 133 away from 140, we end up 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.

Step 10:
The number 19 fits into 70 3 times, leaving a remainder of 13.
The number 3 becomes the next digit in our result. 
Result so far: 6824.9473
If we subtract 57 from 70, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 11:
If we divide 130 by 19, we get 6 and a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 6824.94736
If we subtract 114 from 130, 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.

Advancing to step 12:
160 divided by 19 is 8 with a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 6824.947368
Subtract 152 from 160 to 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 13:
19 goes into 80 4 times with a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 6824.9473684
If we subtract 76 from 80, we 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 14:
The number 19 fits into 40 2 times, leaving a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 6824.94736842
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.

Our division results in 6824.94736842 with a remaining 2e-09.