We're dividing 37303 by 31 
Our goal is to divide 37303 by 31.

On to step 1:
31 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 31

Let's proceed to step 2:
The number 31 fits into 37 1 times, leaving a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 31 from 37 and we're left with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 31

Advancing to step 3:
31 can be fit into 63 2 times, resulting in a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 12.0
If we take 62 away from 63, we end up with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 31

Step 4:
The number 31 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 120.0
Subtracting 0 from 10 leaves us with 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 31

On to step 5:
If we divide 103 by 31, we get 3 and a remainder of 10.
The number 3 becomes the next digit in our result. 
Result so far: 1203.0
If we subtract 93 from 103, 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.

Let's proceed to step 6:
31 can be fit into 100 3 times, resulting in a remainder of 7.
The next digit of our result is 3. 
Result so far: 1203.3
If we subtract 93 from 100, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
When dividing 70 by 31, we get 2 with a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 1203.32
Deduct 62 from 70 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 8:
When dividing 80 by 31, we get 2 with a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 1203.322
Subtract 62 from 80 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

After the division, we end up with 1203.322 and a remainder of 0.0018.