We're dividing 597090 by 45 
We're looking to find how many times 45 goes into 597090.

On to step 1:
The number 45 fits into 5 0 times, leaving a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 45

Let's proceed to step 2:
The number 45 fits into 59 1 times, leaving a remainder of 14.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 45 from 59 leaves us with 14.
Take the next digit (7) from the dividend and append it to 14, then repeat: 147 / 45

On to step 3:
45 goes into 147 3 times with a remainder of 12.
Write down 3 as next digit of the result. 
Result so far: 13.0
Deduct 135 from 147 and we're left with 12.
Bring next digit (0) of the dividend behind the 12 and repeat the process: 120 / 45

Going ahead to step 4:
If we divide 120 by 45, we get 2 and a remainder of 30.
Record the quotient 2 as the next digit in the result. 
Result so far: 132.0
If we take 90 away from 120, we end up with 30.
Take the next digit (9) from the dividend and append it to 30, then repeat: 309 / 45

Let's proceed to step 5:
45 goes into 309 6 times with a remainder of 39.
Use 6 as the next digit of our solution. 
Result so far: 1326.0
Subtract 270 from 309 to get 39.
Bring next digit (0) of the dividend behind the 39 and repeat the process: 390 / 45

Moving on to step 6:
The number 45 fits into 390 8 times, leaving a remainder of 30.
Write down 8 as next digit of the result. 
Result so far: 13268.0
Subtract 360 from 390 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 7:
45 can be fit into 300 6 times, resulting in a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 13268.6
The remainder is 30 after subtracting 270 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 8:
The number 45 fits into 300 6 times, leaving a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 13268.66
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 13268.66 with a balance of 0.03.