We look at the division of 259578 by 45 
We want to figure out the number of times 259578 can be divided by 45.

Step 1:
45 can be fit into 2 0 times, resulting in a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 45

On to step 2:
If we divide 25 by 45, we get 0 and a remainder of 25.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 25 leaves us with 25.
Grab the next digit (9) from the dividend, add it to 25, then carry on: 259 / 45

Going ahead to step 3:
When dividing 259 by 45, we get 5 with a remainder of 34.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Deduct 225 from 259 and we're left with 34.
Bring next digit (5) of the dividend behind the 34 and repeat the process: 345 / 45

Going ahead to step 4:
If we divide 345 by 45, we get 7 and a remainder of 30.
Put 7 as the next digit of the answer. 
Result so far: 57.0
Deduct 315 from 345 and we're left with 30.
Append the next digit (7) from the dividend to 30 and continue with: 307 / 45

Let's proceed to step 5:
45 goes into 307 6 times with a remainder of 37.
Use 6 as the next digit of our solution. 
Result so far: 576.0
The remainder is 37 after subtracting 270 from 307.
Take the next digit (8) from the dividend and append it to 37, then repeat: 378 / 45

Moving on to step 6:
45 goes into 378 8 times with a remainder of 18.
The number 8 becomes the next digit in our result. 
Result so far: 5768.0
Subtract 360 from 378 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 7:
If we divide 180 by 45, we get 4 and a remainder of 0.
Write down 4 as next digit of the result. 
Result so far: 5768.4
Subtracting 180 from 180 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 8:
45 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 5768.4
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 9:
If we divide 0 by 45, we get 0 and a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 5768.4
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Our division results in 5768.4 with a remaining 0.0.