261600 divided by 42 
We're looking to find how many times 42 goes into 261600.

Step 1:
42 can be fit into 2 0 times, resulting in a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 42

Advancing to step 2:
26 divided by 42 is 0 with a remainder of 26.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 26 and we're left with 26.
Take the next digit (1) from the dividend and append it to 26, then repeat: 261 / 42

Advancing to step 3:
When dividing 261 by 42, we get 6 with a remainder of 9.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 9 after subtracting 252 from 261.
Take the next digit (6) from the dividend and append it to 9, then repeat: 96 / 42

Advancing to step 4:
If we divide 96 by 42, we get 2 and a remainder of 12.
Use 2 as the next digit of our solution. 
Result so far: 62.0
Subtract 84 from 96 to get 12.
Bring next digit (0) of the dividend behind the 12 and repeat the process: 120 / 42

Going ahead to step 5:
42 goes into 120 2 times with a remainder of 36.
The next digit of our result is 2. 
Result so far: 622.0
If we take 84 away from 120, we end up with 36.
Append the next digit (0) from the dividend to 36 and continue with: 360 / 42

Advancing to step 6:
If we divide 360 by 42, we get 8 and a remainder of 24.
Use 8 as the next digit of our solution. 
Result so far: 6228.0
If we subtract 336 from 360, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 7:
The number 42 fits into 240 5 times, leaving a remainder of 30.
Record the quotient 5 as the next digit in the result. 
Result so far: 6228.5
The remainder is 30 after subtracting 210 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 8:
The number 42 fits into 300 7 times, leaving a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 6228.57
Subtracting 294 from 300 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.

Moving on to step 9:
If we divide 60 by 42, we get 1 and a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 6228.571
Subtracting 42 from 60 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 10:
42 can be fit into 180 4 times, resulting in a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 6228.5714
Subtracting 168 from 180 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 11:
When dividing 120 by 42, we get 2 with a remainder of 36.
The number 2 becomes the next digit in our result. 
Result so far: 6228.57142
The remainder is 36 after subtracting 84 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Let's proceed to step 12:
42 can be fit into 360 8 times, resulting in a remainder of 24.
The number 8 becomes the next digit in our result. 
Result so far: 6228.571428
Subtracting 336 from 360 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 13:
42 can be fit into 240 5 times, resulting in a remainder of 30.
The next digit of our result is 5. 
Result so far: 6228.5714285
Deduct 210 from 240 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 14:
The number 42 fits into 300 7 times, leaving a remainder of 6.
The next digit of our result is 7. 
Result so far: 6228.57142857
Subtracting 294 from 300 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.

In conclusion, the division gives 6228.57142857 with a balance of 6e-09.