We're dividing 406581 by 59 
We're looking to find how many times 59 goes into 406581.

Let's proceed to step 1:
When dividing 4 by 59, we get 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 59

Step 2:
When dividing 40 by 59, we get 0 with a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 40 to get 40.
Grab the next digit (6) from the dividend, add it to 40, then carry on: 406 / 59

Advancing to step 3:
406 divided by 59 is 6 with a remainder of 52.
The next digit of our result is 6. 
Result so far: 6.0
Subtracting 354 from 406 leaves us with 52.
Take the next digit (5) from the dividend and append it to 52, then repeat: 525 / 59

Let's proceed to step 4:
59 can be fit into 525 8 times, resulting in a remainder of 53.
Record the quotient 8 as the next digit in the result. 
Result so far: 68.0
Deduct 472 from 525 and we're left with 53.
Include the next digit (8) from the dividend after 53, then repeat: 538 / 59

Going ahead to step 5:
538 divided by 59 is 9 with a remainder of 7.
The next digit of our result is 9. 
Result so far: 689.0
If we take 531 away from 538, we end up with 7.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 59

Step 6:
The number 59 fits into 71 1 times, leaving a remainder of 12.
Write down 1 as next digit of the result. 
Result so far: 6891.0
If we take 59 away from 71, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 7:
120 divided by 59 is 2 with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 6891.2
Subtract 118 from 120 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
59 goes into 20 0 times with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 6891.2
Deduct 0 from 20 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 9:
When dividing 200 by 59, we get 3 with a remainder of 23.
Use 3 as the next digit of our solution. 
Result so far: 6891.203
If we take 177 away from 200, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 10:
When dividing 230 by 59, we get 3 with a remainder of 53.
The number 3 becomes the next digit in our result. 
Result so far: 6891.2033
If we subtract 177 from 230, we get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

After the division, we end up with 6891.2033 and a remainder of 0.00053.