419563 ÷ 15 
We want to figure out the number of times 419563 can be divided by 15.

Advancing to step 1:
4 divided by 15 is 0 with 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.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 15

Going ahead to step 2:
The number 15 fits into 41 2 times, leaving a remainder of 11.
The next digit of our result is 2. 
Result so far: 2.0
The remainder is 11 after subtracting 30 from 41.
Append the next digit (9) from the dividend to 11 and continue with: 119 / 15

On to step 3:
119 divided by 15 is 7 with a remainder of 14.
Put 7 as the next digit of the answer. 
Result so far: 27.0
The remainder is 14 after subtracting 105 from 119.
Fetch the next digit (5) from the dividend, attach it to 14 and continue: 145 / 15

Going ahead to step 4:
15 can be fit into 145 9 times, resulting in a remainder of 10.
Record the quotient 9 as the next digit in the result. 
Result so far: 279.0
If we subtract 135 from 145, we get 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 15

Going ahead to step 5:
The number 15 fits into 106 7 times, leaving a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 2797.0
Subtracting 105 from 106 leaves us with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 15

Going ahead to step 6:
15 goes into 13 0 times with a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 27970.0
The remainder is 13 after subtracting 0 from 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 7:
The number 15 fits into 130 8 times, leaving a remainder of 10.
Put 8 as the next digit of the answer. 
Result so far: 27970.8
Subtract 120 from 130 to 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 8:
100 divided by 15 is 6 with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 27970.86
If we subtract 90 from 100, 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.

Going ahead to step 9:
15 goes into 100 6 times with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 27970.866
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 27970.866 with a balance of 0.001.