We look at the division of 137109 by 42 
We want to figure out the number of times 137109 can be divided by 42.

Moving on to step 1:
1 divided by 42 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 42

Going ahead to step 2:
42 can be fit into 13 0 times, resulting in a remainder of 13.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 13, we get 13.
Bring next digit (7) of the dividend behind the 13 and repeat the process: 137 / 42

Let's proceed to step 3:
If we divide 137 by 42, we get 3 and a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we subtract 126 from 137, we get 11.
Grab the next digit (1) from the dividend, add it to 11, then carry on: 111 / 42

Advancing to step 4:
111 divided by 42 is 2 with a remainder of 27.
The number 2 becomes the next digit in our result. 
Result so far: 32.0
Subtract 84 from 111 to get 27.
Append the next digit (0) from the dividend to 27 and continue with: 270 / 42

Moving on to step 5:
270 divided by 42 is 6 with a remainder of 18.
Use 6 as the next digit of our solution. 
Result so far: 326.0
Subtract 252 from 270 to get 18.
Fetch the next digit (9) from the dividend, attach it to 18 and continue: 189 / 42

Advancing to step 6:
42 can be fit into 189 4 times, resulting in a remainder of 21.
Record the quotient 4 as the next digit in the result. 
Result so far: 3264.0
Subtract 168 from 189 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
The number 42 fits into 210 5 times, leaving a remainder of 0.
The next digit of our result is 5. 
Result so far: 3264.5
If we take 210 away from 210, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 8:
If we divide 0 by 42, we get 0 and a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 3264.5
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 9:
42 goes into 0 0 times with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 3264.5
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 3264.5, and the remainder is 0.0.