We're dividing 705407 by 65 
We're looking to find how many times 65 goes into 705407.

Step 1:
7 divided by 65 is 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Fetch the next digit (0) from the dividend, attach it to 7 and continue: 70 / 65

On to step 2:
When dividing 70 by 65, we get 1 with a remainder of 5.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 65 from 70, we get 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 65

Going ahead to step 3:
65 can be fit into 55 0 times, resulting in a remainder of 55.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we subtract 0 from 55, we get 55.
Append the next digit (4) from the dividend to 55 and continue with: 554 / 65

Step 4:
The number 65 fits into 554 8 times, leaving a remainder of 34.
The next digit of our result is 8. 
Result so far: 108.0
Subtract 520 from 554 to get 34.
Bring next digit (0) of the dividend behind the 34 and repeat the process: 340 / 65

Step 5:
65 can be fit into 340 5 times, resulting in a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 1085.0
Subtract 325 from 340 to get 15.
Include the next digit (7) from the dividend after 15, then repeat: 157 / 65

Moving on to step 6:
If we divide 157 by 65, we get 2 and a remainder of 27.
Record the quotient 2 as the next digit in the result. 
Result so far: 10852.0
Deduct 130 from 157 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 7:
65 can be fit into 270 4 times, resulting in a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 10852.4
Subtract 260 from 270 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 8:
65 goes into 100 1 times with a remainder of 35.
The next digit of our result is 1. 
Result so far: 10852.41
If we take 65 away from 100, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 9:
When dividing 350 by 65, we get 5 with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 10852.415
Deduct 325 from 350 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 10:
65 goes into 250 3 times with a remainder of 55.
The next digit of our result is 3. 
Result so far: 10852.4153
Subtract 195 from 250 to get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 11:
When dividing 550 by 65, we get 8 with a remainder of 30.
The next digit of our result is 8. 
Result so far: 10852.41538
The remainder is 30 after subtracting 520 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 12:
65 goes into 300 4 times with a remainder of 40.
The next digit of our result is 4. 
Result so far: 10852.415384
If we subtract 260 from 300, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 13:
If we divide 400 by 65, we get 6 and a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 10852.4153846
If we take 390 away from 400, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 14:
65 can be fit into 100 1 times, resulting in a remainder of 35.
The number 1 becomes the next digit in our result. 
Result so far: 10852.41538461
Subtracting 65 from 100 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

The quotient of the division is 10852.41538461, and the remainder is 3.5e-08.