34406 ÷ 61 
We want to figure out the number of times 34406 can be divided by 61.

On to step 1:
If we divide 3 by 61, we get 0 and a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 61

Advancing to step 2:
The number 61 fits into 34 0 times, leaving a remainder of 34.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 34 after subtracting 0 from 34.
Take the next digit (4) from the dividend and append it to 34, then repeat: 344 / 61

Advancing to step 3:
When dividing 344 by 61, we get 5 with a remainder of 39.
The next digit of our result is 5. 
Result so far: 5.0
If we take 305 away from 344, we end up with 39.
Include the next digit (0) from the dividend after 39, then repeat: 390 / 61

On to step 4:
If we divide 390 by 61, we get 6 and a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 56.0
If we take 366 away from 390, we end up with 24.
Append the next digit (6) from the dividend to 24 and continue with: 246 / 61

Moving on to step 5:
246 divided by 61 is 4 with a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 564.0
The remainder is 2 after subtracting 244 from 246.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 6:
If we divide 20 by 61, we get 0 and a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 564.0
Deduct 0 from 20 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.

Moving on to step 7:
The number 61 fits into 200 3 times, leaving a remainder of 17.
The next digit of our result is 3. 
Result so far: 564.03
Deduct 183 from 200 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Step 8:
61 goes into 170 2 times with a remainder of 48.
Record the quotient 2 as the next digit in the result. 
Result so far: 564.032
Deduct 122 from 170 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Step 9:
The number 61 fits into 480 7 times, leaving a remainder of 53.
Record the quotient 7 as the next digit in the result. 
Result so far: 564.0327
Deduct 427 from 480 and we're left with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Let's proceed to step 10:
530 divided by 61 is 8 with a remainder of 42.
The number 8 becomes the next digit in our result. 
Result so far: 564.03278
If we subtract 488 from 530, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 11:
The number 61 fits into 420 6 times, leaving a remainder of 54.
Put 6 as the next digit of the answer. 
Result so far: 564.032786
The remainder is 54 after subtracting 366 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Advancing to step 12:
61 can be fit into 540 8 times, resulting in a remainder of 52.
Put 8 as the next digit of the answer. 
Result so far: 564.0327868
If we subtract 488 from 540, we 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.

Going ahead to step 13:
The number 61 fits into 520 8 times, leaving a remainder of 32.
Put 8 as the next digit of the answer. 
Result so far: 564.03278688
The remainder is 32 after subtracting 488 from 520.
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 564.03278688 with a balance of 3.2e-08.