145784 divided by 45 
We want to figure out the number of times 145784 can be divided by 45.

Moving on to step 1:
When dividing 1 by 45, we get 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 45

Advancing to step 2:
45 can be fit into 14 0 times, resulting in a remainder of 14.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 14 after subtracting 0 from 14.
Append the next digit (5) from the dividend to 14 and continue with: 145 / 45

On to step 3:
45 can be fit into 145 3 times, resulting in a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 3.0
If we take 135 away from 145, we end up with 10.
Take the next digit (7) from the dividend and append it to 10, then repeat: 107 / 45

Moving on to step 4:
45 goes into 107 2 times with a remainder of 17.
Use 2 as the next digit of our solution. 
Result so far: 32.0
Subtract 90 from 107 to get 17.
Append the next digit (8) from the dividend to 17 and continue with: 178 / 45

Advancing to step 5:
178 divided by 45 is 3 with a remainder of 43.
Put 3 as the next digit of the answer. 
Result so far: 323.0
Deduct 135 from 178 and we're left with 43.
Fetch the next digit (4) from the dividend, attach it to 43 and continue: 434 / 45

On to step 6:
The number 45 fits into 434 9 times, leaving a remainder of 29.
Put 9 as the next digit of the answer. 
Result so far: 3239.0
The remainder is 29 after subtracting 405 from 434.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 7:
The number 45 fits into 290 6 times, leaving a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 3239.6
Subtracting 270 from 290 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
The number 45 fits into 200 4 times, leaving a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 3239.64
If we take 180 away from 200, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 9:
200 divided by 45 is 4 with a remainder of 20.
Record the quotient 4 as the next digit in the result. 
Result so far: 3239.644
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The quotient of the division is 3239.644, and the remainder is 0.002.