645457 ÷ 41 
Our goal is to divide 645457 by 41.

Going ahead to step 1:
41 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 41

On to step 2:
41 goes into 64 1 times with a remainder of 23.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 41 from 64, we get 23.
Take the next digit (5) from the dividend and append it to 23, then repeat: 235 / 41

On to step 3:
41 can be fit into 235 5 times, resulting in a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 15.0
If we subtract 205 from 235, we get 30.
Bring next digit (4) of the dividend behind the 30 and repeat the process: 304 / 41

Going ahead to step 4:
304 divided by 41 is 7 with a remainder of 17.
The next digit of our result is 7. 
Result so far: 157.0
If we take 287 away from 304, we end up with 17.
Include the next digit (5) from the dividend after 17, then repeat: 175 / 41

Moving on to step 5:
41 goes into 175 4 times with a remainder of 11.
Put 4 as the next digit of the answer. 
Result so far: 1574.0
If we subtract 164 from 175, we get 11.
Grab the next digit (7) from the dividend, add it to 11, then carry on: 117 / 41

Let's proceed to step 6:
41 can be fit into 117 2 times, resulting in a remainder of 35.
The number 2 becomes the next digit in our result. 
Result so far: 15742.0
Deduct 82 from 117 and we're left 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.

Let's proceed to step 7:
41 can be fit into 350 8 times, resulting in a remainder of 22.
The next digit of our result is 8. 
Result so far: 15742.8
Subtract 328 from 350 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 8:
The number 41 fits into 220 5 times, leaving a remainder of 15.
The next digit of our result is 5. 
Result so far: 15742.85
Subtract 205 from 220 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 9:
150 divided by 41 is 3 with a remainder of 27.
Put 3 as the next digit of the answer. 
Result so far: 15742.853
The remainder is 27 after subtracting 123 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 10:
41 goes into 270 6 times with a remainder of 24.
The next digit of our result is 6. 
Result so far: 15742.8536
If we subtract 246 from 270, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 11:
The number 41 fits into 240 5 times, leaving a remainder of 35.
The next digit of our result is 5. 
Result so far: 15742.85365
Subtract 205 from 240 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 12:
41 can be fit into 350 8 times, resulting in a remainder of 22.
The next digit of our result is 8. 
Result so far: 15742.853658
The remainder is 22 after subtracting 328 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 13:
41 can be fit into 220 5 times, resulting in a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 15742.8536585
The remainder is 15 after subtracting 205 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 14:
41 goes into 150 3 times with a remainder of 27.
Write down 3 as next digit of the result. 
Result so far: 15742.85365853
If we take 123 away from 150, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

The quotient of the division is 15742.85365853, and the remainder is 2.7e-08.