We're dividing 137262 by 34 
We want to figure out the number of times 137262 can be divided by 34.

Let's proceed to step 1:
34 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 34

Going ahead to step 2:
If we divide 13 by 34, we get 0 and a remainder of 13.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 13 leaves us with 13.
Bring next digit (7) of the dividend behind the 13 and repeat the process: 137 / 34

Moving on to step 3:
34 goes into 137 4 times with a remainder of 1.
The next digit of our result is 4. 
Result so far: 4.0
If we take 136 away from 137, we end up with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 34

Let's proceed to step 4:
34 goes into 12 0 times with a remainder of 12.
Use 0 as the next digit of our solution. 
Result so far: 40.0
If we subtract 0 from 12, we get 12.
Bring next digit (6) of the dividend behind the 12 and repeat the process: 126 / 34

Let's proceed to step 5:
126 divided by 34 is 3 with a remainder of 24.
The next digit of our result is 3. 
Result so far: 403.0
The remainder is 24 after subtracting 102 from 126.
Grab the next digit (2) from the dividend, add it to 24, then carry on: 242 / 34

Going ahead to step 6:
The number 34 fits into 242 7 times, leaving a remainder of 4.
Write down 7 as next digit of the result. 
Result so far: 4037.0
Subtracting 238 from 242 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
When dividing 40 by 34, we get 1 with a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 4037.1
Subtracting 34 from 40 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.

On to step 8:
34 goes into 60 1 times with a remainder of 26.
Record the quotient 1 as the next digit in the result. 
Result so far: 4037.11
Subtracting 34 from 60 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The quotient of the division is 4037.11, and the remainder is 0.026.