30419 ÷ 72 
Our goal is to divide 30419 by 72.

Going ahead to step 1:
72 goes into 3 0 times with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Grab the next digit (0) from the dividend, add it to 3, then carry on: 30 / 72

Going ahead to step 2:
When dividing 30 by 72, we get 0 with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 30 after subtracting 0 from 30.
Include the next digit (4) from the dividend after 30, then repeat: 304 / 72

Going ahead to step 3:
The number 72 fits into 304 4 times, leaving a remainder of 16.
Use 4 as the next digit of our solution. 
Result so far: 4.0
If we subtract 288 from 304, we get 16.
Grab the next digit (1) from the dividend, add it to 16, then carry on: 161 / 72

Step 4:
72 goes into 161 2 times with a remainder of 17.
The number 2 becomes the next digit in our result. 
Result so far: 42.0
If we take 144 away from 161, we end up with 17.
Append the next digit (9) from the dividend to 17 and continue with: 179 / 72

On to step 5:
179 divided by 72 is 2 with a remainder of 35.
Record the quotient 2 as the next digit in the result. 
Result so far: 422.0
Subtracting 144 from 179 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 6:
If we divide 350 by 72, we get 4 and a remainder of 62.
Use 4 as the next digit of our solution. 
Result so far: 422.4
The remainder is 62 after subtracting 288 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Step 7:
72 goes into 620 8 times with a remainder of 44.
Write down 8 as next digit of the result. 
Result so far: 422.48
If we subtract 576 from 620, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 8:
If we divide 440 by 72, we get 6 and a remainder of 8.
The number 6 becomes the next digit in our result. 
Result so far: 422.486
If we take 432 away from 440, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 9:
80 divided by 72 is 1 with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 422.4861
Deduct 72 from 80 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 10:
72 can be fit into 80 1 times, resulting in a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 422.48611
If we take 72 away from 80, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The final result is 422.48611 with a remainder of 8e-06.