414174 ÷ 39 
We want to figure out the number of times 414174 can be divided by 39.

Going ahead to step 1:
When dividing 4 by 39, we get 0 with 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.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 39

Let's proceed to step 2:
When dividing 41 by 39, we get 1 with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 39 from 41 to get 2.
Include the next digit (4) from the dividend after 2, then repeat: 24 / 39

Let's proceed to step 3:
If we divide 24 by 39, we get 0 and a remainder of 24.
Write down 0 as next digit of the result. 
Result so far: 10.0
If we take 0 away from 24, we end up with 24.
Include the next digit (1) from the dividend after 24, then repeat: 241 / 39

On to step 4:
241 divided by 39 is 6 with a remainder of 7.
The number 6 becomes the next digit in our result. 
Result so far: 106.0
If we take 234 away from 241, we end up with 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 39

On to step 5:
If we divide 77 by 39, we get 1 and a remainder of 38.
Record the quotient 1 as the next digit in the result. 
Result so far: 1061.0
Deduct 39 from 77 and we're left with 38.
Grab the next digit (4) from the dividend, add it to 38, then carry on: 384 / 39

Advancing to step 6:
39 can be fit into 384 9 times, resulting in a remainder of 33.
Write down 9 as next digit of the result. 
Result so far: 10619.0
If we subtract 351 from 384, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 7:
When dividing 330 by 39, we get 8 with a remainder of 18.
The next digit of our result is 8. 
Result so far: 10619.8
If we subtract 312 from 330, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 8:
The number 39 fits into 180 4 times, leaving a remainder of 24.
Put 4 as the next digit of the answer. 
Result so far: 10619.84
Subtract 156 from 180 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 9:
When dividing 240 by 39, we get 6 with a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 10619.846
If we subtract 234 from 240, we 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.

Step 10:
60 divided by 39 is 1 with a remainder of 21.
Write down 1 as next digit of the result. 
Result so far: 10619.8461
If we take 39 away from 60, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 11:
When dividing 210 by 39, we get 5 with a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 10619.84615
Subtracting 195 from 210 leaves us 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.

Let's proceed to step 12:
If we divide 150 by 39, we get 3 and a remainder of 33.
The next digit of our result is 3. 
Result so far: 10619.846153
The remainder is 33 after subtracting 117 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 13:
39 can be fit into 330 8 times, resulting in a remainder of 18.
Record the quotient 8 as the next digit in the result. 
Result so far: 10619.8461538
If we take 312 away from 330, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 14:
If we divide 180 by 39, we get 4 and a remainder of 24.
Record the quotient 4 as the next digit in the result. 
Result so far: 10619.84615384
Deduct 156 from 180 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

In conclusion, the division gives 10619.84615384 with a balance of 2.4e-08.