We look at the division of 637517 by 3 
We're looking to find how many times 3 goes into 637517.

Moving on to step 1:
When dividing 6 by 3, we get 2 with a remainder of 0.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Deduct 6 from 6 and we're left with 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 3

Moving on to step 2:
The number 3 fits into 3 1 times, leaving a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 21.0
Subtracting 3 from 3 leaves us with 0.
Append the next digit (7) from the dividend to 0 and continue with: 7 / 3

Let's proceed to step 3:
If we divide 7 by 3, we get 2 and a remainder of 1.
The number 2 becomes the next digit in our result. 
Result so far: 212.0
The remainder is 1 after subtracting 6 from 7.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

Advancing to step 4:
15 divided by 3 is 5 with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 2125.0
The remainder is 0 after subtracting 15 from 15.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 3

Step 5:
3 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 21250.0
If we take 0 away from 1, we end up with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 3

On to step 6:
When dividing 17 by 3, we get 5 with a remainder of 2.
The next digit of our result is 5. 
Result so far: 212505.0
If we take 15 away from 17, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 7:
20 divided by 3 is 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 212505.6
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
3 goes into 20 6 times with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 212505.66
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 212505.66 and a remainder of 0.002.