261865 divided by 42 
We want to figure out the number of times 261865 can be divided by 42.

On to step 1:
When dividing 2 by 42, we get 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 42

Step 2:
If we divide 26 by 42, we get 0 and a remainder of 26.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 26, we get 26.
Include the next digit (1) from the dividend after 26, then repeat: 261 / 42

Going ahead to step 3:
42 goes into 261 6 times with a remainder of 9.
The next digit of our result is 6. 
Result so far: 6.0
Subtract 252 from 261 to get 9.
Append the next digit (8) from the dividend to 9 and continue with: 98 / 42

On to step 4:
The number 42 fits into 98 2 times, leaving a remainder of 14.
The next digit of our result is 2. 
Result so far: 62.0
Subtracting 84 from 98 leaves us with 14.
Grab the next digit (6) from the dividend, add it to 14, then carry on: 146 / 42

Advancing to step 5:
42 can be fit into 146 3 times, resulting in a remainder of 20.
Use 3 as the next digit of our solution. 
Result so far: 623.0
Deduct 126 from 146 and we're left with 20.
Take the next digit (5) from the dividend and append it to 20, then repeat: 205 / 42

Let's proceed to step 6:
205 divided by 42 is 4 with a remainder of 37.
Use 4 as the next digit of our solution. 
Result so far: 6234.0
Subtracting 168 from 205 leaves us with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Step 7:
370 divided by 42 is 8 with a remainder of 34.
Record the quotient 8 as the next digit in the result. 
Result so far: 6234.8
If we take 336 away from 370, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 8:
42 can be fit into 340 8 times, resulting in a remainder of 4.
Put 8 as the next digit of the answer. 
Result so far: 6234.88
If we subtract 336 from 340, 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.

The final result is 6234.88 with a remainder of 0.004.