We look at the division of 419776 by 65 
Our goal is to divide 419776 by 65.

Moving on to step 1:
65 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 65

On to step 2:
When dividing 41 by 65, we get 0 with a remainder of 41.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 41 and we're left with 41.
Grab the next digit (9) from the dividend, add it to 41, then carry on: 419 / 65

Advancing to step 3:
The number 65 fits into 419 6 times, leaving a remainder of 29.
The next digit of our result is 6. 
Result so far: 6.0
If we subtract 390 from 419, we get 29.
Fetch the next digit (7) from the dividend, attach it to 29 and continue: 297 / 65

Moving on to step 4:
The number 65 fits into 297 4 times, leaving a remainder of 37.
Use 4 as the next digit of our solution. 
Result so far: 64.0
If we take 260 away from 297, we end up with 37.
Include the next digit (7) from the dividend after 37, then repeat: 377 / 65

Step 5:
65 can be fit into 377 5 times, resulting in a remainder of 52.
The number 5 becomes the next digit in our result. 
Result so far: 645.0
Subtracting 325 from 377 leaves us with 52.
Grab the next digit (6) from the dividend, add it to 52, then carry on: 526 / 65

Going ahead to step 6:
The number 65 fits into 526 8 times, leaving a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 6458.0
Subtract 520 from 526 to get 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 7:
60 divided by 65 is 0 with a remainder of 60.
Use 0 as the next digit of our solution. 
Result so far: 6458.0
If we subtract 0 from 60, 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.

Going ahead to step 8:
If we divide 600 by 65, we get 9 and a remainder of 15.
Put 9 as the next digit of the answer. 
Result so far: 6458.09
Deduct 585 from 600 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.

Step 9:
The number 65 fits into 150 2 times, leaving a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 6458.092
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.

On to step 10:
If we divide 200 by 65, we get 3 and a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 6458.0923
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.

Step 11:
The number 65 fits into 50 0 times, leaving a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 6458.0923
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.

Moving on to step 12:
500 divided by 65 is 7 with a remainder of 45.
Use 7 as the next digit of our solution. 
Result so far: 6458.092307
Deduct 455 from 500 and we're left 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.

On to step 13:
If we divide 450 by 65, we get 6 and a remainder of 60.
Write down 6 as next digit of the result. 
Result so far: 6458.0923076
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 14:
When dividing 600 by 65, we get 9 with a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 6458.09230769
Deduct 585 from 600 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.

The quotient of the division is 6458.09230769, and the remainder is 1.5e-08.