41421136 ÷ 679 
Our goal is to divide 41421136 by 679.

On to step 1:
4 divided by 679 is 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 679

On to step 2:
If we divide 41 by 679, we get 0 and a remainder of 41.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 41 and we're left with 41.
Append the next digit (4) from the dividend to 41 and continue with: 414 / 679

Moving on to step 3:
679 can be fit into 414 0 times, resulting in a remainder of 414.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 414, we get 414.
Take the next digit (2) from the dividend and append it to 414, then repeat: 4142 / 679

Going ahead to step 4:
679 goes into 4142 6 times with a remainder of 68.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 4074 from 4142 and we're left with 68.
Take the next digit (1) from the dividend and append it to 68, then repeat: 681 / 679

Moving on to step 5:
When dividing 681 by 679, we get 1 with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 61.0
The remainder is 2 after subtracting 679 from 681.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 679

Moving on to step 6:
21 divided by 679 is 0 with a remainder of 21.
Write down 0 as next digit of the result. 
Result so far: 610.0
If we subtract 0 from 21, we get 21.
Take the next digit (3) from the dividend and append it to 21, then repeat: 213 / 679

On to step 7:
When dividing 213 by 679, we get 0 with a remainder of 213.
Put 0 as the next digit of the answer. 
Result so far: 6100.0
If we take 0 away from 213, we end up with 213.
Bring next digit (6) of the dividend behind the 213 and repeat the process: 2136 / 679

Step 8:
If we divide 2136 by 679, we get 3 and a remainder of 99.
Put 3 as the next digit of the answer. 
Result so far: 61003.0
The remainder is 99 after subtracting 2037 from 2136.
Since there are no more digits in the dividend, we add a zero to the remainder making it 990, and continue the process.

Going ahead to step 9:
679 goes into 990 1 times with a remainder of 311.
Write down 1 as next digit of the result. 
Result so far: 61003.1
If we subtract 679 from 990, we get 311.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3110, and continue the process.

Let's proceed to step 10:
679 goes into 3110 4 times with a remainder of 394.
Record the quotient 4 as the next digit in the result. 
Result so far: 61003.14
The remainder is 394 after subtracting 2716 from 3110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3940, and continue the process.

Step 11:
If we divide 3940 by 679, we get 5 and a remainder of 545.
The next digit of our result is 5. 
Result so far: 61003.145
Subtract 3395 from 3940 to get 545.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5450, and continue the process.

Advancing to step 12:
If we divide 5450 by 679, we get 8 and a remainder of 18.
The number 8 becomes the next digit in our result. 
Result so far: 61003.1458
Deduct 5432 from 5450 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 13:
679 goes into 180 0 times with a remainder of 180.
Use 0 as the next digit of our solution. 
Result so far: 61003.1458
If we take 0 away from 180, we end up with 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1800, and continue the process.

Moving on to step 14:
1800 divided by 679 is 2 with a remainder of 442.
The number 2 becomes the next digit in our result. 
Result so far: 61003.145802
If we subtract 1358 from 1800, we get 442.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4420, and continue the process.

Advancing to step 15:
When dividing 4420 by 679, we get 6 with a remainder of 346.
Record the quotient 6 as the next digit in the result. 
Result so far: 61003.1458026
The remainder is 346 after subtracting 4074 from 4420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3460, and continue the process.

Step 16:
The number 679 fits into 3460 5 times, leaving a remainder of 65.
Use 5 as the next digit of our solution. 
Result so far: 61003.14580265
Subtract 3395 from 3460 to get 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The quotient of the division is 61003.14580265, and the remainder is 6.5e-08.