We're dividing 589742 by 45 
Our goal is to divide 589742 by 45.

On to step 1:
If we divide 5 by 45, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 45

Let's proceed to step 2:
The number 45 fits into 58 1 times, leaving a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 45 away from 58, we end up with 13.
Take the next digit (9) from the dividend and append it to 13, then repeat: 139 / 45

Step 3:
If we divide 139 by 45, we get 3 and a remainder of 4.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 135 away from 139, we end up with 4.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 45

Moving on to step 4:
47 divided by 45 is 1 with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 131.0
The remainder is 2 after subtracting 45 from 47.
Grab the next digit (4) from the dividend, add it to 2, then carry on: 24 / 45

On to step 5:
45 can be fit into 24 0 times, resulting in a remainder of 24.
The next digit of our result is 0. 
Result so far: 1310.0
If we take 0 away from 24, we end up with 24.
Fetch the next digit (2) from the dividend, attach it to 24 and continue: 242 / 45

Let's proceed to step 6:
When dividing 242 by 45, we get 5 with a remainder of 17.
Write down 5 as next digit of the result. 
Result so far: 13105.0
Subtracting 225 from 242 leaves us 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.

Advancing to step 7:
45 can be fit into 170 3 times, resulting in a remainder of 35.
Record the quotient 3 as the next digit in the result. 
Result so far: 13105.3
Deduct 135 from 170 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 8:
350 divided by 45 is 7 with a remainder of 35.
Write down 7 as next digit of the result. 
Result so far: 13105.37
If we take 315 away from 350, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 9:
If we divide 350 by 45, we get 7 and a remainder of 35.
The number 7 becomes the next digit in our result. 
Result so far: 13105.377
Subtract 315 from 350 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

The final outcome is 13105.377, with a leftover of 0.0035.