738633 ÷ 45 
Our goal is to divide 738633 by 45.

Let's proceed to step 1:
7 divided by 45 is 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Take the next digit (3) from the dividend and append it to 7, then repeat: 73 / 45

Advancing to step 2:
The number 45 fits into 73 1 times, leaving a remainder of 28.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 45 from 73 to get 28.
Include the next digit (8) from the dividend after 28, then repeat: 288 / 45

Step 3:
When dividing 288 by 45, we get 6 with a remainder of 18.
The number 6 becomes the next digit in our result. 
Result so far: 16.0
Subtracting 270 from 288 leaves us with 18.
Grab the next digit (6) from the dividend, add it to 18, then carry on: 186 / 45

Going ahead to step 4:
45 goes into 186 4 times with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 164.0
Deduct 180 from 186 and we're left with 6.
Append the next digit (3) from the dividend to 6 and continue with: 63 / 45

Step 5:
63 divided by 45 is 1 with a remainder of 18.
Record the quotient 1 as the next digit in the result. 
Result so far: 1641.0
Deduct 45 from 63 and we're left with 18.
Bring next digit (3) of the dividend behind the 18 and repeat the process: 183 / 45

On to step 6:
45 goes into 183 4 times with a remainder of 3.
Write down 4 as next digit of the result. 
Result so far: 16414.0
The remainder is 3 after subtracting 180 from 183.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 7:
30 divided by 45 is 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 16414.0
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
300 divided by 45 is 6 with a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 16414.06
Subtract 270 from 300 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 9:
The number 45 fits into 300 6 times, leaving a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 16414.066
If we take 270 away from 300, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The final result is 16414.066 with a remainder of 0.003.