We look at the division of 419338 by 24 
We want to figure out the number of times 419338 can be divided by 24.

Step 1:
24 can be fit into 4 0 times, resulting in 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.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 24

On to step 2:
When dividing 41 by 24, we get 1 with a remainder of 17.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 17 after subtracting 24 from 41.
Include the next digit (9) from the dividend after 17, then repeat: 179 / 24

On to step 3:
The number 24 fits into 179 7 times, leaving a remainder of 11.
The number 7 becomes the next digit in our result. 
Result so far: 17.0
If we subtract 168 from 179, we get 11.
Grab the next digit (3) from the dividend, add it to 11, then carry on: 113 / 24

Step 4:
The number 24 fits into 113 4 times, leaving a remainder of 17.
The number 4 becomes the next digit in our result. 
Result so far: 174.0
Deduct 96 from 113 and we're left with 17.
Grab the next digit (3) from the dividend, add it to 17, then carry on: 173 / 24

On to step 5:
The number 24 fits into 173 7 times, leaving a remainder of 5.
Write down 7 as next digit of the result. 
Result so far: 1747.0
Deduct 168 from 173 and we're left with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 24

Step 6:
When dividing 58 by 24, we get 2 with a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 17472.0
If we take 48 away from 58, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 7:
The number 24 fits into 100 4 times, leaving a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 17472.4
Deduct 96 from 100 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 8:
When dividing 40 by 24, we get 1 with a remainder of 16.
Record the quotient 1 as the next digit in the result. 
Result so far: 17472.41
Subtract 24 from 40 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 9:
24 goes into 160 6 times with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 17472.416
If we take 144 away from 160, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 10:
24 goes into 160 6 times with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 17472.4166
Subtracting 144 from 160 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final result is 17472.4166 with a remainder of 0.00016.