We look at the division of 754259 by 45 
We're looking to find how many times 45 goes into 754259.

Let's proceed to step 1:
If we divide 7 by 45, we get 0 and a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Include the next digit (5) from the dividend after 7, then repeat: 75 / 45

Let's proceed to step 2:
The number 45 fits into 75 1 times, leaving a remainder of 30.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 45 from 75 leaves us with 30.
Append the next digit (4) from the dividend to 30 and continue with: 304 / 45

Moving on to step 3:
The number 45 fits into 304 6 times, leaving a remainder of 34.
Use 6 as the next digit of our solution. 
Result so far: 16.0
The remainder is 34 after subtracting 270 from 304.
Include the next digit (2) from the dividend after 34, then repeat: 342 / 45

Step 4:
When dividing 342 by 45, we get 7 with a remainder of 27.
Put 7 as the next digit of the answer. 
Result so far: 167.0
The remainder is 27 after subtracting 315 from 342.
Append the next digit (5) from the dividend to 27 and continue with: 275 / 45

Let's proceed to step 5:
45 goes into 275 6 times with a remainder of 5.
Write down 6 as next digit of the result. 
Result so far: 1676.0
If we subtract 270 from 275, we get 5.
Fetch the next digit (9) from the dividend, attach it to 5 and continue: 59 / 45

Let's proceed to step 6:
45 goes into 59 1 times with a remainder of 14.
The number 1 becomes the next digit in our result. 
Result so far: 16761.0
Subtracting 45 from 59 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 7:
The number 45 fits into 140 3 times, leaving a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 16761.3
Deduct 135 from 140 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 8:
When dividing 50 by 45, we get 1 with a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 16761.31
Subtract 45 from 50 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 9:
The number 45 fits into 50 1 times, leaving a remainder of 5.
The next digit of our result is 1. 
Result so far: 16761.311
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

In conclusion, the division gives 16761.311 with a balance of 0.0005.