113365 ÷ 45 
Let's see how many times 45 fits into 113365.

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.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 45

On to step 2:
11 divided by 45 is 0 with a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 11 leaves us with 11.
Take the next digit (3) from the dividend and append it to 11, then repeat: 113 / 45

Moving on to step 3:
45 goes into 113 2 times with a remainder of 23.
Write down 2 as next digit of the result. 
Result so far: 2.0
If we take 90 away from 113, we end up with 23.
Append the next digit (3) from the dividend to 23 and continue with: 233 / 45

Step 4:
When dividing 233 by 45, we get 5 with a remainder of 8.
The number 5 becomes the next digit in our result. 
Result so far: 25.0
If we subtract 225 from 233, we get 8.
Grab the next digit (6) from the dividend, add it to 8, then carry on: 86 / 45

Let's proceed to step 5:
When dividing 86 by 45, we get 1 with a remainder of 41.
Write down 1 as next digit of the result. 
Result so far: 251.0
Deduct 45 from 86 and we're left with 41.
Grab the next digit (5) from the dividend, add it to 41, then carry on: 415 / 45

On to step 6:
If we divide 415 by 45, we get 9 and a remainder of 10.
Put 9 as the next digit of the answer. 
Result so far: 2519.0
The remainder is 10 after subtracting 405 from 415.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 7:
The number 45 fits into 100 2 times, leaving a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 2519.2
If we subtract 90 from 100, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 8:
The number 45 fits into 100 2 times, leaving a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 2519.22
Subtracting 90 from 100 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 2519.22, and the remainder is 0.01.