We look at the division of 42629214 by 588 
We want to figure out the number of times 42629214 can be divided by 588.

Moving on to step 1:
If we divide 4 by 588, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
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 / 588

Moving on to step 2:
The number 588 fits into 42 0 times, leaving a remainder of 42.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Append the next digit (6) from the dividend to 42 and continue with: 426 / 588

Moving on to step 3:
588 can be fit into 426 0 times, resulting in a remainder of 426.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 426 and we're left with 426.
Bring next digit (2) of the dividend behind the 426 and repeat the process: 4262 / 588

Advancing to step 4:
588 goes into 4262 7 times with a remainder of 146.
Write down 7 as next digit of the result. 
Result so far: 7.0
The remainder is 146 after subtracting 4116 from 4262.
Fetch the next digit (9) from the dividend, attach it to 146 and continue: 1469 / 588

Let's proceed to step 5:
The number 588 fits into 1469 2 times, leaving a remainder of 293.
Put 2 as the next digit of the answer. 
Result so far: 72.0
If we subtract 1176 from 1469, we get 293.
Include the next digit (2) from the dividend after 293, then repeat: 2932 / 588

Let's proceed to step 6:
588 goes into 2932 4 times with a remainder of 580.
Write down 4 as next digit of the result. 
Result so far: 724.0
Subtracting 2352 from 2932 leaves us with 580.
Grab the next digit (1) from the dividend, add it to 580, then carry on: 5801 / 588

On to step 7:
5801 divided by 588 is 9 with a remainder of 509.
The number 9 becomes the next digit in our result. 
Result so far: 7249.0
If we take 5292 away from 5801, we end up with 509.
Fetch the next digit (4) from the dividend, attach it to 509 and continue: 5094 / 588

Let's proceed to step 8:
5094 divided by 588 is 8 with a remainder of 390.
Write down 8 as next digit of the result. 
Result so far: 72498.0
If we subtract 4704 from 5094, we get 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3900, and continue the process.

Let's proceed to step 9:
The number 588 fits into 3900 6 times, leaving a remainder of 372.
Put 6 as the next digit of the answer. 
Result so far: 72498.6
Subtract 3528 from 3900 to get 372.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3720, and continue the process.

Let's proceed to step 10:
3720 divided by 588 is 6 with a remainder of 192.
Put 6 as the next digit of the answer. 
Result so far: 72498.66
Deduct 3528 from 3720 and we're left with 192.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1920, and continue the process.

The final outcome is 72498.66, with a leftover of 0.192.