6617569 ÷ 349 
We want to figure out the number of times 6617569 can be divided by 349.

On to step 1:
If we divide 6 by 349, 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.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 349

Going ahead to step 2:
If we divide 66 by 349, we get 0 and a remainder of 66.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 66 after subtracting 0 from 66.
Grab the next digit (1) from the dividend, add it to 66, then carry on: 661 / 349

Step 3:
The number 349 fits into 661 1 times, leaving a remainder of 312.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 349 from 661, we get 312.
Fetch the next digit (7) from the dividend, attach it to 312 and continue: 3127 / 349

Advancing to step 4:
349 can be fit into 3127 8 times, resulting in a remainder of 335.
The next digit of our result is 8. 
Result so far: 18.0
The remainder is 335 after subtracting 2792 from 3127.
Grab the next digit (5) from the dividend, add it to 335, then carry on: 3355 / 349

Advancing to step 5:
349 goes into 3355 9 times with a remainder of 214.
Record the quotient 9 as the next digit in the result. 
Result so far: 189.0
The remainder is 214 after subtracting 3141 from 3355.
Include the next digit (6) from the dividend after 214, then repeat: 2146 / 349

Moving on to step 6:
349 goes into 2146 6 times with a remainder of 52.
Put 6 as the next digit of the answer. 
Result so far: 1896.0
If we subtract 2094 from 2146, we get 52.
Append the next digit (9) from the dividend to 52 and continue with: 529 / 349

Advancing to step 7:
529 divided by 349 is 1 with a remainder of 180.
Write down 1 as next digit of the result. 
Result so far: 18961.0
Subtract 349 from 529 to get 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 8:
The number 349 fits into 1800 5 times, leaving a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 18961.5
Deduct 1745 from 1800 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 9:
When dividing 550 by 349, we get 1 with a remainder of 201.
Record the quotient 1 as the next digit in the result. 
Result so far: 18961.51
The remainder is 201 after subtracting 349 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2010, and continue the process.

Advancing to step 10:
349 can be fit into 2010 5 times, resulting in a remainder of 265.
The number 5 becomes the next digit in our result. 
Result so far: 18961.515
Subtract 1745 from 2010 to get 265.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2650, and continue the process.

On to step 11:
349 goes into 2650 7 times with a remainder of 207.
Record the quotient 7 as the next digit in the result. 
Result so far: 18961.5157
The remainder is 207 after subtracting 2443 from 2650.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2070, and continue the process.

Step 12:
The number 349 fits into 2070 5 times, leaving a remainder of 325.
The number 5 becomes the next digit in our result. 
Result so far: 18961.51575
If we take 1745 away from 2070, we end up with 325.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3250, and continue the process.

Let's proceed to step 13:
349 goes into 3250 9 times with a remainder of 109.
The next digit of our result is 9. 
Result so far: 18961.515759
Deduct 3141 from 3250 and we're left with 109.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1090, and continue the process.

On to step 14:
The number 349 fits into 1090 3 times, leaving a remainder of 43.
The number 3 becomes the next digit in our result. 
Result so far: 18961.5157593
If we take 1047 away from 1090, we end up with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 15:
349 can be fit into 430 1 times, resulting in a remainder of 81.
The next digit of our result is 1. 
Result so far: 18961.51575931
Subtract 349 from 430 to get 81.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

In conclusion, the division gives 18961.51575931 with a balance of 8.1e-08.