259637 ÷ 45 
We want to figure out the number of times 259637 can be divided by 45.

On to step 1:
45 can be fit into 2 0 times, resulting in a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 45

Moving on to step 2:
45 goes into 25 0 times with a remainder of 25.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 25, we end up with 25.
Bring next digit (9) of the dividend behind the 25 and repeat the process: 259 / 45

Moving on to step 3:
259 divided by 45 is 5 with a remainder of 34.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Subtracting 225 from 259 leaves us with 34.
Fetch the next digit (6) from the dividend, attach it to 34 and continue: 346 / 45

On to step 4:
If we divide 346 by 45, we get 7 and a remainder of 31.
Put 7 as the next digit of the answer. 
Result so far: 57.0
The remainder is 31 after subtracting 315 from 346.
Grab the next digit (3) from the dividend, add it to 31, then carry on: 313 / 45

Advancing to step 5:
45 can be fit into 313 6 times, resulting in a remainder of 43.
The number 6 becomes the next digit in our result. 
Result so far: 576.0
The remainder is 43 after subtracting 270 from 313.
Take the next digit (7) from the dividend and append it to 43, then repeat: 437 / 45

Step 6:
45 goes into 437 9 times with a remainder of 32.
Put 9 as the next digit of the answer. 
Result so far: 5769.0
Deduct 405 from 437 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 7:
When dividing 320 by 45, we get 7 with a remainder of 5.
Put 7 as the next digit of the answer. 
Result so far: 5769.7
The remainder is 5 after subtracting 315 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
The number 45 fits into 50 1 times, leaving a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 5769.71
If we take 45 away from 50, we end up 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.

Advancing to step 9:
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: 5769.711
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.

The final outcome is 5769.711, with a leftover of 0.0005.