409181 ÷ 59 
Our goal is to divide 409181 by 59.

Going ahead to step 1:
If we divide 4 by 59, we get 0 and a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 59

Let's proceed to step 2:
59 goes into 40 0 times with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 40 leaves us with 40.
Include the next digit (9) from the dividend after 40, then repeat: 409 / 59

Moving on to step 3:
When dividing 409 by 59, we get 6 with a remainder of 55.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we subtract 354 from 409, we get 55.
Fetch the next digit (1) from the dividend, attach it to 55 and continue: 551 / 59

Let's proceed to step 4:
When dividing 551 by 59, we get 9 with a remainder of 20.
The next digit of our result is 9. 
Result so far: 69.0
If we subtract 531 from 551, we get 20.
Include the next digit (8) from the dividend after 20, then repeat: 208 / 59

Moving on to step 5:
208 divided by 59 is 3 with a remainder of 31.
Put 3 as the next digit of the answer. 
Result so far: 693.0
If we take 177 away from 208, we end up with 31.
Include the next digit (1) from the dividend after 31, then repeat: 311 / 59

Step 6:
When dividing 311 by 59, we get 5 with a remainder of 16.
Put 5 as the next digit of the answer. 
Result so far: 6935.0
Subtract 295 from 311 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 7:
When dividing 160 by 59, we get 2 with a remainder of 42.
Put 2 as the next digit of the answer. 
Result so far: 6935.2
Subtracting 118 from 160 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Step 8:
420 divided by 59 is 7 with a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 6935.27
Subtract 413 from 420 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 9:
59 goes into 70 1 times with a remainder of 11.
Write down 1 as next digit of the result. 
Result so far: 6935.271
If we subtract 59 from 70, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 10:
If we divide 110 by 59, we get 1 and a remainder of 51.
Use 1 as the next digit of our solution. 
Result so far: 6935.2711
Subtracting 59 from 110 leaves us with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

The quotient of the division is 6935.2711, and the remainder is 0.00051.