414665 ÷ 61 
We want to figure out the number of times 414665 can be divided by 61.

Advancing to step 1:
The number 61 fits into 4 0 times, leaving a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 61

Step 2:
If we divide 41 by 61, we get 0 and a remainder of 41.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 41, we end up with 41.
Append the next digit (4) from the dividend to 41 and continue with: 414 / 61

Moving on to step 3:
414 divided by 61 is 6 with a remainder of 48.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 48 after subtracting 366 from 414.
Grab the next digit (6) from the dividend, add it to 48, then carry on: 486 / 61

On to step 4:
61 goes into 486 7 times with a remainder of 59.
Use 7 as the next digit of our solution. 
Result so far: 67.0
Deduct 427 from 486 and we're left with 59.
Grab the next digit (6) from the dividend, add it to 59, then carry on: 596 / 61

Advancing to step 5:
61 can be fit into 596 9 times, resulting in a remainder of 47.
The number 9 becomes the next digit in our result. 
Result so far: 679.0
The remainder is 47 after subtracting 549 from 596.
Take the next digit (5) from the dividend and append it to 47, then repeat: 475 / 61

Step 6:
61 can be fit into 475 7 times, resulting in a remainder of 48.
Write down 7 as next digit of the result. 
Result so far: 6797.0
If we subtract 427 from 475, we get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 7:
480 divided by 61 is 7 with a remainder of 53.
Write down 7 as next digit of the result. 
Result so far: 6797.7
Subtract 427 from 480 to get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Going ahead to step 8:
The number 61 fits into 530 8 times, leaving a remainder of 42.
Write down 8 as next digit of the result. 
Result so far: 6797.78
If we take 488 away from 530, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 9:
420 divided by 61 is 6 with a remainder of 54.
Write down 6 as next digit of the result. 
Result so far: 6797.786
Deduct 366 from 420 and we're left with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

On to step 10:
When dividing 540 by 61, we get 8 with a remainder of 52.
Use 8 as the next digit of our solution. 
Result so far: 6797.7868
Subtract 488 from 540 to get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Let's proceed to step 11:
If we divide 520 by 61, we get 8 and a remainder of 32.
Write down 8 as next digit of the result. 
Result so far: 6797.78688
Deduct 488 from 520 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

In conclusion, the division gives 6797.78688 with a balance of 3.2e-05.