We're dividing 42105 by 65 
We want to figure out the number of times 42105 can be divided by 65.

Step 1:
If we divide 4 by 65, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 65

Advancing to step 2:
When dividing 42 by 65, we get 0 with a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Include the next digit (1) from the dividend after 42, then repeat: 421 / 65

Moving on to step 3:
65 can be fit into 421 6 times, resulting in a remainder of 31.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 390 away from 421, we end up with 31.
Take the next digit (0) from the dividend and append it to 31, then repeat: 310 / 65

On to step 4:
The number 65 fits into 310 4 times, leaving a remainder of 50.
The next digit of our result is 4. 
Result so far: 64.0
If we subtract 260 from 310, we get 50.
Grab the next digit (5) from the dividend, add it to 50, then carry on: 505 / 65

On to step 5:
When dividing 505 by 65, we get 7 with a remainder of 50.
Put 7 as the next digit of the answer. 
Result so far: 647.0
If we subtract 455 from 505, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 6:
65 can be fit into 500 7 times, resulting in a remainder of 45.
The number 7 becomes the next digit in our result. 
Result so far: 647.7
Subtract 455 from 500 to get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Advancing to step 7:
The number 65 fits into 450 6 times, leaving a remainder of 60.
Put 6 as the next digit of the answer. 
Result so far: 647.76
If we subtract 390 from 450, we get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 8:
600 divided by 65 is 9 with a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 647.769
The remainder is 15 after subtracting 585 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 9:
150 divided by 65 is 2 with a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 647.7692
The remainder is 20 after subtracting 130 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 10:
When dividing 200 by 65, we get 3 with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 647.76923
The remainder is 5 after subtracting 195 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
65 can be fit into 50 0 times, resulting in a remainder of 50.
The next digit of our result is 0. 
Result so far: 647.76923
Subtract 0 from 50 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 12:
500 divided by 65 is 7 with a remainder of 45.
Record the quotient 7 as the next digit in the result. 
Result so far: 647.7692307
Subtracting 455 from 500 leaves us with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 13:
When dividing 450 by 65, we get 6 with a remainder of 60.
Put 6 as the next digit of the answer. 
Result so far: 647.76923076
Subtracting 390 from 450 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

The final result is 647.76923076 with a remainder of 6e-08.