Let's divide 31420400 by 603
Our goal is to divide 31420400 by 603.

On to step 1:
When dividing 3 by 603, we get 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (1) from the dividend and append it to 3, then repeat: 31 / 603

Step 2:
When dividing 31 by 603, we get 0 with a remainder of 31.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 31, we end up with 31.
Include the next digit (4) from the dividend after 31, then repeat: 314 / 603

Moving on to step 3:
314 divided by 603 is 0 with a remainder of 314.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 314, we get 314.
Bring next digit (2) of the dividend behind the 314 and repeat the process: 3142 / 603

On to step 4:
603 goes into 3142 5 times with a remainder of 127.
Put 5 as the next digit of the answer. 
Result so far: 5.0
The remainder is 127 after subtracting 3015 from 3142.
Grab the next digit (0) from the dividend, add it to 127, then carry on: 1270 / 603

On to step 5:
1270 divided by 603 is 2 with a remainder of 64.
The next digit of our result is 2. 
Result so far: 52.0
The remainder is 64 after subtracting 1206 from 1270.
Append the next digit (4) from the dividend to 64 and continue with: 644 / 603

On to step 6:
644 divided by 603 is 1 with a remainder of 41.
The number 1 becomes the next digit in our result. 
Result so far: 521.0
If we subtract 603 from 644, we get 41.
Fetch the next digit (0) from the dividend, attach it to 41 and continue: 410 / 603

On to step 7:
603 goes into 410 0 times with a remainder of 410.
Write down 0 as next digit of the result. 
Result so far: 5210.0
Subtract 0 from 410 to get 410.
Fetch the next digit (0) from the dividend, attach it to 410 and continue: 4100 / 603

On to step 8:
4100 divided by 603 is 6 with a remainder of 482.
The next digit of our result is 6. 
Result so far: 52106.0
The remainder is 482 after subtracting 3618 from 4100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4820, and continue the process.

On to step 9:
603 can be fit into 4820 7 times, resulting in a remainder of 599.
Put 7 as the next digit of the answer. 
Result so far: 52106.7
The remainder is 599 after subtracting 4221 from 4820.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5990, and continue the process.

Step 10:
The number 603 fits into 5990 9 times, leaving a remainder of 563.
The next digit of our result is 9. 
Result so far: 52106.79
Deduct 5427 from 5990 and we're left with 563.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5630, and continue the process.

Step 11:
If we divide 5630 by 603, we get 9 and a remainder of 203.
Record the quotient 9 as the next digit in the result. 
Result so far: 52106.799
If we subtract 5427 from 5630, we get 203.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2030, and continue the process.

The quotient of the division is 52106.799, and the remainder is 0.0203.