617584 ÷ 45 
We want to figure out the number of times 617584 can be divided by 45.

On to step 1:
The number 45 fits into 6 0 times, leaving a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (1) from the dividend to 6 and continue with: 61 / 45

Advancing to step 2:
The number 45 fits into 61 1 times, leaving a remainder of 16.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 16 after subtracting 45 from 61.
Append the next digit (7) from the dividend to 16 and continue with: 167 / 45

Going ahead to step 3:
If we divide 167 by 45, we get 3 and a remainder of 32.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 135 away from 167, we end up with 32.
Include the next digit (5) from the dividend after 32, then repeat: 325 / 45

Step 4:
45 goes into 325 7 times with a remainder of 10.
Put 7 as the next digit of the answer. 
Result so far: 137.0
If we subtract 315 from 325, we get 10.
Include the next digit (8) from the dividend after 10, then repeat: 108 / 45

Going ahead to step 5:
108 divided by 45 is 2 with a remainder of 18.
The next digit of our result is 2. 
Result so far: 1372.0
If we subtract 90 from 108, we get 18.
Include the next digit (4) from the dividend after 18, then repeat: 184 / 45

Going ahead to step 6:
When dividing 184 by 45, we get 4 with a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 13724.0
The remainder is 4 after subtracting 180 from 184.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
40 divided by 45 is 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 13724.0
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 8:
45 can be fit into 400 8 times, resulting in a remainder of 40.
Record the quotient 8 as the next digit in the result. 
Result so far: 13724.08
If we take 360 away from 400, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 9:
45 goes into 400 8 times with a remainder of 40.
The number 8 becomes the next digit in our result. 
Result so far: 13724.088
Subtract 360 from 400 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The quotient of the division is 13724.088, and the remainder is 0.004.