We look at the division of 645201 by 61 
We want to figure out the number of times 645201 can be divided by 61.

On to step 1:
61 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 61

Going ahead to step 2:
The number 61 fits into 64 1 times, leaving a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 61 from 64, we get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 61

Going ahead to step 3:
When dividing 35 by 61, we get 0 with a remainder of 35.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we take 0 away from 35, we end up with 35.
Take the next digit (2) from the dividend and append it to 35, then repeat: 352 / 61

On to step 4:
352 divided by 61 is 5 with a remainder of 47.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
Subtract 305 from 352 to get 47.
Bring next digit (0) of the dividend behind the 47 and repeat the process: 470 / 61

Moving on to step 5:
When dividing 470 by 61, we get 7 with a remainder of 43.
The number 7 becomes the next digit in our result. 
Result so far: 1057.0
The remainder is 43 after subtracting 427 from 470.
Fetch the next digit (1) from the dividend, attach it to 43 and continue: 431 / 61

Advancing to step 6:
431 divided by 61 is 7 with a remainder of 4.
Record the quotient 7 as the next digit in the result. 
Result so far: 10577.0
Subtract 427 from 431 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 7:
40 divided by 61 is 0 with a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 10577.0
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 8:
If we divide 400 by 61, we get 6 and a remainder of 34.
Put 6 as the next digit of the answer. 
Result so far: 10577.06
Subtract 366 from 400 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 9:
61 can be fit into 340 5 times, resulting in a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 10577.065
Subtracting 305 from 340 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 10:
61 can be fit into 350 5 times, resulting in a remainder of 45.
Record the quotient 5 as the next digit in the result. 
Result so far: 10577.0655
If we subtract 305 from 350, we get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Our division results in 10577.0655 with a remaining 0.00045.