We're dividing 6661903 by 653 
Let's see how many times 653 fits into 6661903.

Step 1:
If we divide 6 by 653, we get 0 and a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Append the next digit (6) from the dividend to 6 and continue with: 66 / 653

On to step 2:
653 can be fit into 66 0 times, resulting in a remainder of 66.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 66 after subtracting 0 from 66.
Include the next digit (6) from the dividend after 66, then repeat: 666 / 653

Moving on to step 3:
653 can be fit into 666 1 times, resulting in a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 653 from 666 to get 13.
Append the next digit (1) from the dividend to 13 and continue with: 131 / 653

Going ahead to step 4:
653 goes into 131 0 times with a remainder of 131.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Subtract 0 from 131 to get 131.
Bring next digit (9) of the dividend behind the 131 and repeat the process: 1319 / 653

Moving on to step 5:
If we divide 1319 by 653, we get 2 and a remainder of 13.
Use 2 as the next digit of our solution. 
Result so far: 102.0
Subtracting 1306 from 1319 leaves us with 13.
Take the next digit (0) from the dividend and append it to 13, then repeat: 130 / 653

Let's proceed to step 6:
If we divide 130 by 653, we get 0 and a remainder of 130.
Put 0 as the next digit of the answer. 
Result so far: 1020.0
If we subtract 0 from 130, we get 130.
Append the next digit (3) from the dividend to 130 and continue with: 1303 / 653

Advancing to step 7:
1303 divided by 653 is 1 with a remainder of 650.
Put 1 as the next digit of the answer. 
Result so far: 10201.0
Subtracting 653 from 1303 leaves us with 650.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6500, and continue the process.

Moving on to step 8:
653 goes into 6500 9 times with a remainder of 623.
The next digit of our result is 9. 
Result so far: 10201.9
If we subtract 5877 from 6500, we get 623.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6230, and continue the process.

Advancing to step 9:
The number 653 fits into 6230 9 times, leaving a remainder of 353.
Record the quotient 9 as the next digit in the result. 
Result so far: 10201.99
Subtracting 5877 from 6230 leaves us with 353.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3530, and continue the process.

After the division, we end up with 10201.99 and a remainder of 0.353.