We're dividing 274565 by 42 
We want to divide 274565 by 42.

Step 1:
2 divided by 42 is 0 with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 42

Let's proceed to step 2:
42 goes into 27 0 times with a remainder of 27.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 27 after subtracting 0 from 27.
Bring next digit (4) of the dividend behind the 27 and repeat the process: 274 / 42

On to step 3:
274 divided by 42 is 6 with a remainder of 22.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtract 252 from 274 to get 22.
Bring next digit (5) of the dividend behind the 22 and repeat the process: 225 / 42

On to step 4:
42 goes into 225 5 times with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 65.0
Subtract 210 from 225 to get 15.
Include the next digit (6) from the dividend after 15, then repeat: 156 / 42

On to step 5:
42 goes into 156 3 times with a remainder of 30.
Write down 3 as next digit of the result. 
Result so far: 653.0
If we take 126 away from 156, we end up with 30.
Append the next digit (5) from the dividend to 30 and continue with: 305 / 42

Let's proceed to step 6:
42 goes into 305 7 times with a remainder of 11.
Record the quotient 7 as the next digit in the result. 
Result so far: 6537.0
If we take 294 away from 305, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 7:
42 can be fit into 110 2 times, resulting in a remainder of 26.
The next digit of our result is 2. 
Result so far: 6537.2
Subtract 84 from 110 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 8:
42 goes into 260 6 times with a remainder of 8.
The number 6 becomes the next digit in our result. 
Result so far: 6537.26
If we take 252 away from 260, we end up 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.

Let's proceed to step 9:
When dividing 80 by 42, we get 1 with a remainder of 38.
Put 1 as the next digit of the answer. 
Result so far: 6537.261
Deduct 42 from 80 and we're left with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 10:
The number 42 fits into 380 9 times, leaving a remainder of 2.
The next digit of our result is 9. 
Result so far: 6537.2619
Subtracting 378 from 380 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.

Going ahead to step 11:
When dividing 20 by 42, we get 0 with a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 6537.2619
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 12:
200 divided by 42 is 4 with a remainder of 32.
Record the quotient 4 as the next digit in the result. 
Result so far: 6537.261904
If we subtract 168 from 200, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 13:
When dividing 320 by 42, we get 7 with a remainder of 26.
The number 7 becomes the next digit in our result. 
Result so far: 6537.2619047
Deduct 294 from 320 and we're left 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.

Moving on to step 14:
42 goes into 260 6 times with a remainder of 8.
The number 6 becomes the next digit in our result. 
Result so far: 6537.26190476
The remainder is 8 after subtracting 252 from 260.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

In conclusion, the division gives 6537.26190476 with a balance of 8e-09.