137635 divided by 19 
Let's see how many times 19 fits into 137635.

Advancing to step 1:
The number 19 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 19

On to step 2:
19 goes into 13 0 times with a remainder of 13.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Take the next digit (7) from the dividend and append it to 13, then repeat: 137 / 19

Advancing to step 3:
19 goes into 137 7 times with a remainder of 4.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
The remainder is 4 after subtracting 133 from 137.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 19

Step 4:
When dividing 46 by 19, we get 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 72.0
Deduct 38 from 46 and we're left with 8.
Append the next digit (3) from the dividend to 8 and continue with: 83 / 19

Going ahead to step 5:
When dividing 83 by 19, we get 4 with a remainder of 7.
Use 4 as the next digit of our solution. 
Result so far: 724.0
Deduct 76 from 83 and we're left with 7.
Append the next digit (5) from the dividend to 7 and continue with: 75 / 19

On to step 6:
75 divided by 19 is 3 with a remainder of 18.
The next digit of our result is 3. 
Result so far: 7243.0
If we subtract 57 from 75, 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.

Let's proceed to step 7:
19 can be fit into 180 9 times, resulting in a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 7243.9
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.

Going ahead to step 8:
If we divide 90 by 19, we get 4 and a remainder of 14.
Put 4 as the next digit of the answer. 
Result so far: 7243.94
Subtract 76 from 90 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 9:
If we divide 140 by 19, we get 7 and a remainder of 7.
The next digit of our result is 7. 
Result so far: 7243.947
Subtract 133 from 140 to 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.

Moving on to step 10:
70 divided by 19 is 3 with a remainder of 13.
The next digit of our result is 3. 
Result so far: 7243.9473
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.

Let's proceed to step 11:
19 goes into 130 6 times with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 7243.94736
Subtract 114 from 130 to 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 12:
If we divide 160 by 19, we get 8 and a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 7243.947368
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 13:
If we divide 80 by 19, we get 4 and a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 7243.9473684
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.

Advancing to step 14:
19 can be fit into 40 2 times, resulting in a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 7243.94736842
Subtracting 38 from 40 leaves us 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.

After the division, we end up with 7243.94736842 and a remainder of 2e-09.