420137 ÷ 30 
We want to figure out the number of times 420137 can be divided by 30.

Going ahead to step 1:
The number 30 fits into 4 0 times, leaving a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 30

Advancing to step 2:
30 can be fit into 42 1 times, resulting in a remainder of 12.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 30 from 42 leaves us with 12.
Include the next digit (0) from the dividend after 12, then repeat: 120 / 30

Advancing to step 3:
120 divided by 30 is 4 with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 14.0
If we take 120 away from 120, we end up with 0.
Include the next digit (1) from the dividend after 0, then repeat: 1 / 30

Going ahead to step 4:
When dividing 1 by 30, we get 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 140.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 30

Moving on to step 5:
When dividing 13 by 30, we get 0 with a remainder of 13.
The next digit of our result is 0. 
Result so far: 1400.0
Deduct 0 from 13 and we're left with 13.
Include the next digit (7) from the dividend after 13, then repeat: 137 / 30

On to step 6:
If we divide 137 by 30, we get 4 and a remainder of 17.
The next digit of our result is 4. 
Result so far: 14004.0
Deduct 120 from 137 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.

Let's proceed to step 7:
If we divide 170 by 30, we get 5 and a remainder of 20.
The number 5 becomes the next digit in our result. 
Result so far: 14004.5
If we take 150 away from 170, we end up 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.

On to step 8:
If we divide 200 by 30, we get 6 and a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 14004.56
If we take 180 away from 200, we end up 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.

Let's proceed to step 9:
The number 30 fits into 200 6 times, leaving a remainder of 20.
The next digit of our result is 6. 
Result so far: 14004.566
If we take 180 away from 200, we end up 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.

Our division results in 14004.566 with a remaining 0.002.