434646 ÷ 65 
We want to divide 434646 by 65.

Let's proceed to step 1:
If we divide 4 by 65, we get 0 and a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Fetch the next digit (3) from the dividend, attach it to 4 and continue: 43 / 65

Step 2:
If we divide 43 by 65, we get 0 and a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 43, we get 43.
Append the next digit (4) from the dividend to 43 and continue with: 434 / 65

Let's proceed to step 3:
When dividing 434 by 65, we get 6 with a remainder of 44.
Use 6 as the next digit of our solution. 
Result so far: 6.0
The remainder is 44 after subtracting 390 from 434.
Include the next digit (6) from the dividend after 44, then repeat: 446 / 65

Step 4:
446 divided by 65 is 6 with a remainder of 56.
The number 6 becomes the next digit in our result. 
Result so far: 66.0
If we take 390 away from 446, we end up with 56.
Include the next digit (4) from the dividend after 56, then repeat: 564 / 65

Moving on to step 5:
When dividing 564 by 65, we get 8 with a remainder of 44.
Use 8 as the next digit of our solution. 
Result so far: 668.0
The remainder is 44 after subtracting 520 from 564.
Grab the next digit (6) from the dividend, add it to 44, then carry on: 446 / 65

Going ahead to step 6:
446 divided by 65 is 6 with a remainder of 56.
Use 6 as the next digit of our solution. 
Result so far: 6686.0
If we take 390 away from 446, we end up with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

On to step 7:
The number 65 fits into 560 8 times, leaving a remainder of 40.
Use 8 as the next digit of our solution. 
Result so far: 6686.8
Subtract 520 from 560 to 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.

Moving on to step 8:
65 can be fit into 400 6 times, resulting in a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 6686.86
The remainder is 10 after subtracting 390 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 9:
65 can be fit into 100 1 times, resulting in a remainder of 35.
Write down 1 as next digit of the result. 
Result so far: 6686.861
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 10:
350 divided by 65 is 5 with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 6686.8615
Subtracting 325 from 350 leaves us 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.

Moving on to step 11:
When dividing 250 by 65, we get 3 with a remainder of 55.
The number 3 becomes the next digit in our result. 
Result so far: 6686.86153
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.

Going ahead to step 12:
65 goes into 550 8 times with a remainder of 30.
Write down 8 as next digit of the result. 
Result so far: 6686.861538
If we take 520 away from 550, we end up 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 13:
If we divide 300 by 65, we get 4 and a remainder of 40.
The number 4 becomes the next digit in our result. 
Result so far: 6686.8615384
Deduct 260 from 300 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 14:
65 goes into 400 6 times with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 6686.86153846
The remainder is 10 after subtracting 390 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The final outcome is 6686.86153846, with a leftover of 1e-08.