We're dividing 4342629 by 561 
We're looking to find how many times 561 goes into 4342629.

Moving on to step 1:
561 can be fit into 4 0 times, resulting in a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 561

Advancing to step 2:
The number 561 fits into 43 0 times, leaving a remainder of 43.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 43 after subtracting 0 from 43.
Fetch the next digit (4) from the dividend, attach it to 43 and continue: 434 / 561

Let's proceed to step 3:
If we divide 434 by 561, we get 0 and a remainder of 434.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 434 after subtracting 0 from 434.
Grab the next digit (2) from the dividend, add it to 434, then carry on: 4342 / 561

Moving on to step 4:
The number 561 fits into 4342 7 times, leaving a remainder of 415.
Write down 7 as next digit of the result. 
Result so far: 7.0
Subtract 3927 from 4342 to get 415.
Take the next digit (6) from the dividend and append it to 415, then repeat: 4156 / 561

On to step 5:
561 can be fit into 4156 7 times, resulting in a remainder of 229.
The number 7 becomes the next digit in our result. 
Result so far: 77.0
If we take 3927 away from 4156, we end up with 229.
Take the next digit (2) from the dividend and append it to 229, then repeat: 2292 / 561

Going ahead to step 6:
2292 divided by 561 is 4 with a remainder of 48.
Write down 4 as next digit of the result. 
Result so far: 774.0
Subtract 2244 from 2292 to get 48.
Take the next digit (9) from the dividend and append it to 48, then repeat: 489 / 561

Let's proceed to step 7:
561 goes into 489 0 times with a remainder of 489.
Use 0 as the next digit of our solution. 
Result so far: 7740.0
The remainder is 489 after subtracting 0 from 489.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4890, and continue the process.

Going ahead to step 8:
When dividing 4890 by 561, we get 8 with a remainder of 402.
Write down 8 as next digit of the result. 
Result so far: 7740.8
Deduct 4488 from 4890 and we're left with 402.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4020, and continue the process.

Moving on to step 9:
When dividing 4020 by 561, we get 7 with a remainder of 93.
The next digit of our result is 7. 
Result so far: 7740.87
Subtract 3927 from 4020 to get 93.
Since there are no more digits in the dividend, we add a zero to the remainder making it 930, and continue the process.

On to step 10:
If we divide 930 by 561, we get 1 and a remainder of 369.
Use 1 as the next digit of our solution. 
Result so far: 7740.871
Deduct 561 from 930 and we're left with 369.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3690, and continue the process.

Let's proceed to step 11:
3690 divided by 561 is 6 with a remainder of 324.
The next digit of our result is 6. 
Result so far: 7740.8716
If we take 3366 away from 3690, we end up with 324.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3240, and continue the process.

Step 12:
When dividing 3240 by 561, we get 5 with a remainder of 435.
The next digit of our result is 5. 
Result so far: 7740.87165
The remainder is 435 after subtracting 2805 from 3240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4350, and continue the process.

Advancing to step 13:
561 goes into 4350 7 times with a remainder of 423.
The number 7 becomes the next digit in our result. 
Result so far: 7740.871657
Subtract 3927 from 4350 to get 423.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4230, and continue the process.

Step 14:
4230 divided by 561 is 7 with a remainder of 303.
The number 7 becomes the next digit in our result. 
Result so far: 7740.8716577
The remainder is 303 after subtracting 3927 from 4230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3030, and continue the process.

Our division results in 7740.8716577 with a remaining 3.03e-06.