419011 ÷ 65 
Our goal is to divide 419011 by 65.

Let's proceed to step 1:
65 can be fit into 4 0 times, resulting in a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 65

Step 2:
65 can be fit into 41 0 times, resulting in a remainder of 41.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 41 to get 41.
Grab the next digit (9) from the dividend, add it to 41, then carry on: 419 / 65

Step 3:
When dividing 419 by 65, we get 6 with a remainder of 29.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtract 390 from 419 to get 29.
Include the next digit (0) from the dividend after 29, then repeat: 290 / 65

Going ahead to step 4:
65 goes into 290 4 times with a remainder of 30.
Use 4 as the next digit of our solution. 
Result so far: 64.0
Subtract 260 from 290 to get 30.
Include the next digit (1) from the dividend after 30, then repeat: 301 / 65

Moving on to step 5:
301 divided by 65 is 4 with a remainder of 41.
Record the quotient 4 as the next digit in the result. 
Result so far: 644.0
If we subtract 260 from 301, we get 41.
Append the next digit (1) from the dividend to 41 and continue with: 411 / 65

Advancing to step 6:
When dividing 411 by 65, we get 6 with a remainder of 21.
Record the quotient 6 as the next digit in the result. 
Result so far: 6446.0
Subtract 390 from 411 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Let's proceed to step 7:
The number 65 fits into 210 3 times, leaving a remainder of 15.
The next digit of our result is 3. 
Result so far: 6446.3
Deduct 195 from 210 and we're left with 15.
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 8:
65 goes into 150 2 times with a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 6446.32
If we take 130 away from 150, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 9:
When dividing 200 by 65, we get 3 with a remainder of 5.
The next digit of our result is 3. 
Result so far: 6446.323
Subtract 195 from 200 to get 5.
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 10:
If we divide 50 by 65, we get 0 and a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 6446.323
If we subtract 0 from 50, 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.

Let's proceed to step 11:
500 divided by 65 is 7 with a remainder of 45.
Put 7 as the next digit of the answer. 
Result so far: 6446.32307
If we take 455 away from 500, we end up 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.

Step 12:
When dividing 450 by 65, we get 6 with a remainder of 60.
Use 6 as the next digit of our solution. 
Result so far: 6446.323076
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.

On to step 13:
The number 65 fits into 600 9 times, leaving a remainder of 15.
Write down 9 as next digit of the result. 
Result so far: 6446.3230769
If we take 585 away from 600, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 14:
65 can be fit into 150 2 times, resulting in a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 6446.32307692
Deduct 130 from 150 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

In conclusion, the division gives 6446.32307692 with a balance of 2e-08.