We're dividing 645364 by 42 
We're looking to find how many times 42 goes into 645364.

Step 1:
42 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 42

Advancing to step 2:
The number 42 fits into 64 1 times, leaving a remainder of 22.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 22 after subtracting 42 from 64.
Append the next digit (5) from the dividend to 22 and continue with: 225 / 42

Moving on to step 3:
If we divide 225 by 42, we get 5 and a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
The remainder is 15 after subtracting 210 from 225.
Take the next digit (3) from the dividend and append it to 15, then repeat: 153 / 42

Moving on to step 4:
When dividing 153 by 42, we get 3 with a remainder of 27.
Use 3 as the next digit of our solution. 
Result so far: 153.0
If we take 126 away from 153, we end up with 27.
Bring next digit (6) of the dividend behind the 27 and repeat the process: 276 / 42

Advancing to step 5:
When dividing 276 by 42, we get 6 with a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 1536.0
Subtract 252 from 276 to get 24.
Bring next digit (4) of the dividend behind the 24 and repeat the process: 244 / 42

Let's proceed to step 6:
If we divide 244 by 42, we get 5 and a remainder of 34.
The next digit of our result is 5. 
Result so far: 15365.0
If we subtract 210 from 244, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 7:
42 can be fit into 340 8 times, resulting in a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 15365.8
The remainder is 4 after subtracting 336 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 8:
40 divided by 42 is 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 15365.8
If we take 0 away from 40, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 9:
If we divide 400 by 42, we get 9 and a remainder of 22.
Record the quotient 9 as the next digit in the result. 
Result so far: 15365.809
Subtract 378 from 400 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 10:
When dividing 220 by 42, we get 5 with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 15365.8095
Deduct 210 from 220 and we're left 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 11:
When dividing 100 by 42, we get 2 with a remainder of 16.
Write down 2 as next digit of the result. 
Result so far: 15365.80952
Subtract 84 from 100 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.

On to step 12:
The number 42 fits into 160 3 times, leaving a remainder of 34.
Record the quotient 3 as the next digit in the result. 
Result so far: 15365.809523
If we take 126 away from 160, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 13:
42 goes into 340 8 times with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 15365.8095238
If we take 336 away from 340, we end up 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.

Advancing to step 14:
The number 42 fits into 40 0 times, leaving a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 15365.8095238
If we take 0 away from 40, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

In conclusion, the division gives 15365.8095238 with a balance of 4e-08.