6609771 divided by 590 
We want to figure out the number of times 6609771 can be divided by 590.

Advancing to step 1:
If we divide 6 by 590, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 590

Moving on to step 2:
When dividing 66 by 590, we get 0 with a remainder of 66.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 66 to get 66.
Include the next digit (0) from the dividend after 66, then repeat: 660 / 590

Let's proceed to step 3:
When dividing 660 by 590, we get 1 with a remainder of 70.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 590 from 660 to get 70.
Bring next digit (9) of the dividend behind the 70 and repeat the process: 709 / 590

Step 4:
If we divide 709 by 590, we get 1 and a remainder of 119.
Write down 1 as next digit of the result. 
Result so far: 11.0
If we take 590 away from 709, we end up with 119.
Include the next digit (7) from the dividend after 119, then repeat: 1197 / 590

On to step 5:
1197 divided by 590 is 2 with a remainder of 17.
Record the quotient 2 as the next digit in the result. 
Result so far: 112.0
If we take 1180 away from 1197, we end up with 17.
Fetch the next digit (7) from the dividend, attach it to 17 and continue: 177 / 590

Moving on to step 6:
The number 590 fits into 177 0 times, leaving a remainder of 177.
Record the quotient 0 as the next digit in the result. 
Result so far: 1120.0
Deduct 0 from 177 and we're left with 177.
Take the next digit (1) from the dividend and append it to 177, then repeat: 1771 / 590

Step 7:
When dividing 1771 by 590, we get 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 11203.0
If we take 1770 away from 1771, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 8:
590 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 11203.0
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 9:
100 divided by 590 is 0 with a remainder of 100.
The next digit of our result is 0. 
Result so far: 11203.0
Subtract 0 from 100 to get 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1000, and continue the process.

In conclusion, the division gives 11203.0 with a balance of 0.1.