301503 ÷ 45 
We're looking to find how many times 45 goes into 301503.

Step 1:
When dividing 3 by 45, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 45

On to step 2:
45 can be fit into 30 0 times, resulting in a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 30 after subtracting 0 from 30.
Include the next digit (1) from the dividend after 30, then repeat: 301 / 45

Going ahead to step 3:
301 divided by 45 is 6 with a remainder of 31.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 270 away from 301, we end up with 31.
Take the next digit (5) from the dividend and append it to 31, then repeat: 315 / 45

Step 4:
When dividing 315 by 45, we get 7 with a remainder of 0.
Record the quotient 7 as the next digit in the result. 
Result so far: 67.0
Subtracting 315 from 315 leaves us with 0.
Fetch the next digit (0) from the dividend, attach it to 0 and continue: 0 / 45

On to step 5:
If we divide 0 by 45, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 670.0
Deduct 0 from 0 and we're left with 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 45

Step 6:
When dividing 3 by 45, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 6700.0
If we take 0 away from 3, we end up with 3.
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:
45 can be fit into 30 0 times, resulting in a remainder of 30.
The number 0 becomes the next digit in our result. 
Result so far: 6700.0
If we subtract 0 from 30, we 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.

Going ahead to step 8:
If we divide 300 by 45, we get 6 and a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 6700.06
If we subtract 270 from 300, we 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:
300 divided by 45 is 6 with a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 6700.066
Deduct 270 from 300 and we're left 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 6700.066 with a remainder of 0.003.